The draft was initially planned for submission on Friday. It will need the approval of at least 330 members of parliament before it can be put to the popular vote. AKP and Nationalist Movement Party (MHP) supporting the amendment currently have 355 seats in the parliament.
On Friday, Deputy Prime Minister Nurettin Canikli said the referendum may be held in March-April next year.
The controversial bill seeks to give President Recep Tayyip Erdogan sweeping powers in a move described as a power-grab by the opposition Republican People's Party and the pro-Kurdish Peoples' Democratic Party.
In its founding principles, the 1982 constitution asserts that Turkey is a secular, democratic republic. The constitution’s Article 4 bans any modifications to these founding principles.