Megrahi was released from prison in Scotland last month on compassionate grounds because he has terminal prostate cancer and is not expected to live for much longer, British Telegraph reported
The United States, and opposition parties in Britain, have criticised the decision to release him.
Earlier this week a Libyan official said Megrahi had been admitted to an emergency unit at the Tripoli Medical Centre and that his condition was poor.
However, he has now been moved from the unit, suggesting his condition has stabilised.
"Mr Megrahi is out of the emergency room and intensive care but is under close observation by a team of doctors," the hospital source said.
"The hospital has formed a committee to assess his state of health and plans to issue a statement either tomorrow or the day after tomorrow."
The source did not say why Megrahi had been in the emergency unit and did not provide further details about his condition.
Megrahi was the only person convicted over the bombing of Pan Am flight 103 above the Scottish town of Lockerbie, in which 270 people were killed, the majority of which were US citizens.
He received a rapturous welcome when he arrived home in Libya last month.
American President Barack Obama said the release of Megrahi, a former Libyan intelligence agent, was a mistake.
The British government has also been accused by domestic opponents of backing Megrahi's release in a drive to improve ties with Libya, where British firms are seeking greater access to the North African state's oil and gas reserves.