Parliament, where his ruling AK party has a big majority, elects the president.
Erdogan told a gathering of AK parliamentarians: "After all our research and discussions for the 11th president, our dear foreign minister Abdullah Gul has been proposed for the presidency."
Gul is a respected diplomat, who has overseen the launch of European Union accession talks as foreign minister.
Senior members of the AK party, which has roots in political Islam, have said they are concerned that they would lose votes in a November general election if Erdogan, Turkey's most charismatic politician, became president and quit party politics.
Erdogan has never said he would run but had strongly hinted at the possibility.
April 25 is the deadline for registration of candidates. Parliament will begin the first round of votes on April 27. The key vote will be held on May 9.
Elections for parliament are due in November.
The constitution says the president must remain impartial and cannot get involved in national politics, which would bar Erdogan from campaigning.
Pressure had mounted on the government in recent weeks.
Earlier this month, more than 350,000 people rallied in Ankara against a possible Erdogan presidency.
Erdogan is accused of undermining secularism by, for example, trying to ease restrictions on the Muslim headscarf and promoting religious supporters in the bureaucracy.
The armed forces chief General Yasar Buyukanit and outgoing president Ahmet Necdet Sezer have warned of threats posed to the republic in comments seen as warnings to Erdogan.