Speaking to reporters in the capital Ankara Wednesday, the Justice and Development (AK) Party Deputy Chairman Yasin Aktay said the two leaders were expected to announce a joint declaration.
Aktay said the details of the draft constitution were still being worked out, adding an agreed text was likely to be declared at the end of the meeting.
According to the prime ministry sources, who spoke on condition of anonymity, the two leaders will meet at Cankaya Palace at 2 p.m (1100 GMT).
The government has long sought to replace the current parliamentary system with a presidential one, saying there are flaws in the set up, which also holds back Turkey’s development.
Last month, Yildirim said a committee within the AK Party had completed its work on a draft constitution that also included items for a presidential system.
The proposed changes would be put to a public referendum even if the government got the necessary votes in parliament to avoid the need for one, Yildirim had said.
The new constitutional draft needs 330 votes to pave the way for a referendum.
The AK Party, with 316 seats, and the MHP, with 40, both back the bill.