Even though Morsi has only been in power for a few months, there are already strong signs a partnership with Turkey is forming, evidenced by a common effort to end Syria's civil war by urging the exit of President Bashar Assad from power.
Earlier this month, Turkish Foreign Minister Ahmet Davutoglu visited the Egyptian capital Cairo and pledged $2 billion in aid to boost confidence in an economy badly battered by a tourism slump, strikes and ongoing protests since the fall of authoritarian leader Hosni Mubarak in an uprising last year.
During the 12-hour visit, Morsi will try to strengthen economic ties with Turkey - a country his Muslim Brotherhood group views as an Islamist success story, mixing a strong economy with Western ties and Islamic piety.
Turkey, a NATO member with a mostly Muslim, but not Arab, population, has been touted as a democratic model for Egypt and other Arab countries swept up in popular revolts over the past two years.
After initially looking to the Turkish ruling party as a role model, the Islamic fundamentalist Brotherhood in Egypt has cooled to the idea because of Turkey's strong secular leanings. Morsi and the Brotherhood, on the contrary, have been criticized by their opponents for pushing a more conservative Islamist line, particularly in drafting the country's new constitution.
"Before the revolution, we saw (Turkish Prime Minister Recep Tayyip) Erdogan's regime ... as a successful model that can be emulated," said Dina Zakaria, a member of the foreign relations committee of the Muslim Brotherhood's Freedom and Justice Party. "But can it be with all its details and can it all suit Egyptian society? Of course not."
Turkish officials and media have voiced enthusiasm for the relationship with Cairo after the uprising. Turkish President Abdullah Gul was the first foreign leader to visit Egypt after Mubarak stepped down on Feb. 11, 2011, meeting with both the largely liberal and secular youth groups that spearheaded the pro-democracy revolt as well as with generals from the ruling military council who took over from Mubarak and then eventually transferred power to the democratically elected Morsi.
Erdogan got a warm welcome in Cairo last year, with crowds of Brotherhood supporters lining the airport road upon his arrival, some of them carrying banners reading: "Erdogan is a hero."
Erdogan has encouraged Egypt to mimic the Turkish model of governance.
But Zakaria said that after frequent visits to Turkey and meetings with different groups there, she is convinced Egyptian society would not accept Turkey's secular constitution.
Many in conservative Egypt equate the term secularism with "anti-Islam." As efforts to draft the country's constitution are marred by disputes over what many liberals perceive as overtly Islamist clauses in the charter, Zakaria ruled out drawing inspiration from the Turkish constitution.
"Their constitution won't work here in Egypt," she said. "There are things Egyptian people won't accept," she added, referring mainly to the separation of religion and he state.
One of the founding principles of Turkey's constitution is that it is a secular democracy, something that contradicts Egypt's old constitution, and is not even considered in the writing of the new charter. Debate remains in Egypt over whether to keep the current charter, which cites the principles of Islamic law as the basis of legislation, or to harden it to include a reference to specific Islamic laws which would guide all legislation.
But when it comes to foreign affairs and economics, there is much that Egypt can gain from Turkey's experience, Zakaria said.
Certainly on the international stage, Cairo and Ankara have much in common. Both want Assad of Syria to quit and Iran, his ally, to stay out of the civil war there. Ankara and Cairo have teamed as part of a regional initiative to try to solve the Syrian crisis, an effort that could form a strong foundation of future cooperation.
"Turkey couldn't do anything alone when it comes to Syria. One hand alone won't clap," Zakaria said. "What is clear now is that the two countries need to have strong relations because we have serious regional problems and we need each other."
Mustafa Ellabbad, an Egyptian expert on Turkish relations, said Turkey wants an Arab partner in its bid for regional influence in the Middle East and its affiliation with the Brotherhood would serve as a foundation for a moderate Islamist alliance. The Brotherhood, in return, looks to Turkey for assistance as a bridge to the West. But for some of Egypt's more radical Islamists, "the Turkish model doesn't even deserve to be labeled Islamic," Ellabbad said.
But Morsi could turn to Turkey for help on other domestic issues, chief among them the economy. He has already visited Saudi Arabia, Ethiopia, China, Iran, Italy and Belgium before his recent trip to New York, where he addressed the U.N. General Assembly. His frequent travels have raised criticism that he is paying more attention to foreign policy issues than domestic problems. However, the economic issues appear high on the agenda on most of his foreign trips.
"The economic portfolio is certainly one of the most important ones between Egypt and Turkey," Yasser Ali, the presidential spokesman, said Saturday.
Egypt's economy is faltering under the weight of shrinking foreign investment and numerous labor strikes demanding better wages and representation in state-owned companies. The political system remains far from stable, and a referendum on a new constitution and new parliamentary elections that will follow that will test the performance of the Brotherhood's Islamist politics.
This is where Morsi may turn to Turkey for inspiration.
Erdogan's Justice and Development Party, or AKP, has had an extraordinary record of electoral success and longevity, coming to power in 2002 amid economic hardship and a fractured political landscape, and then comfortably winning general elections again in 2007 and 2011.
Zakaria could not confirm local media reports that the AKP provided assistance to the Brotherhood's political party ahead of Egypt's parliamentary elections last year. Brotherhood officials told Egyptian media that the party's local branch in Alexandria, Egypt's second largest city, signed a partnership deal with the AKP in Istanbul, ahead of last winter's parliamentary elections.
Morsi is also expected to attend the annual congress of Turkey's ruling Justice and Development Party, a first for an Egyptian leader, and is invited to attend an economic forum organized by the Turkish chamber of commerce on Sunday.
Hassan Malek, a prominent businessman from the Muslim Brotherhood traveling to Turkey with Morsi, said there is much that Egypt can learn from Turkey in the fields of manufacturing, industry and trade zones. He said Egypt could particularly benefit in the fields of manufacturing apparel, and electronics.
Egypt's Minister of Economic Cooperation Ashraf el-Araby told local media that a committee at the level of prime ministers will be formed to push economic cooperation, including opening the African market for both countries. Trade between the two countries has already reached $3.8 billion in the first nine months of 2012, a 27 percent increase compared to the same period last year, said Turkey's ambassador to Egypt Hussein Awny. He estimated the figure could rise to reach $5 billion by the end of the year.
"It is not hidden that there is a meeting of minds. Geographically we are close, we have similar visions," Malek said. "This is a new opportunity. There are many things in the Turkish experience we can transfer and benefit from. But we can't copy everything."