The constitutional change, which has been sought by Erdogan since he became president in 2014, would see Turkey switch to an executive presidency along the lines of the United States or France.
His supporters say it will streamline the political system but it has become the latest polarising issue surrounding the Turkish strongman.
Erdogan has been accused by domestic rivals and foreign critics of increasingly authoritarian rule, especially after an attempted military coup in July.
The proposal was presented to parliament, the official news agency Anadolu reported, after months of talks between the ruling Justice and Development Party (AKP) led by Prime Minister Binali Yildirim and the Nationalist Movement Party (MHP).
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The MHP is the fourth largest party in parliament but the AKP needs its support for the 330 votes required to call a referendum to approve the issue.
Erdogan said he hoped the bill would receive enough votes in the 550-seat parliament to then put it to the public.
The AKP has only 316 seats (excluding the speaker of the parliament) and needs at least 14 votes from the MHP to secure a three-fifths majority required to call the referendum.
Deputy Prime Minister Nurettin Canikli said yesterday "consensus had been secured" between the MHP and AKP and a referendum could take place in March, April or May.
The main opposition Republican People's Party (CHP) and the pro-Kurdish Peoples' Democratic Party (HDP) vehemently oppose changing the parliamentary system.
CHP leader Kemal Kilicdaroglu said the changes risked wrecking the parliamentary system that goes back to reforms in the late Ottoman Empire.
"This is a regime change, not a system change," Kilicdaroglu said
Erdogan became president in August 2014 after more than a decade as premier and immediately revamped an office which had until then had been seen as largely ceremonial.
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