In a speech to delegates at the opening of the UEFA Congress, Erdogan said: "I would like to repeat the request to host the European Championship in Istanbul in 2020."
The proposal comes as Turkish footballing authorities grapple with a match-fixing investigation, under which 93 people including the chairman of champions Fenerbahce are currently being tried in an Istanbul court.
UEFA will formally start the bidding process next week when all 53 nations will be invited to apply for what is generally regarded as the world's third biggest sports event after the summer Olympic Games and the World Cup.
The tournament, which was first staged with four teams in 1960, will have 24 finalists from 2016 onwards which limits the number of countries who can stage it single-handedly.
Turkey lost out by a single vote to France in a bid to stage the 2016 finals but since then it has also expressed its wish to stage the 2020 summer Olympics and would unlikely be in a position to host both events in the same year.
Earlier this year sports minister Suat Kılıç said that Turkey was concentrating its efforts on an Olympic bid.