In a sign of Mr Davutoglu’s weakening influence, he was stripped last week of the authority to appoint provincial AK Party officials.
Turkish media reported that Mr Davutoglu would hold a news conference on Thursday following a gathering of the party’s central executive committee.
The development comes at a time of increasing instability for Turkey, which is tackling an escalating conflict with the rebels of the Kurdistan Workers’ Party (PKK), terror attacks by the so-called Islamic State, and an influx of migrants and refugees.
Turkey is also in the midst of implementing a key deal with the European Union, brokered by Mr Davutoglu, to limit the number of refugees flowing across its border in return for accelerated EU accession talks and financial aid.
The future of that agreement, which Mr Davutoglu was seen as having agreed with little input from the president, could be plunged into doubt by his departure.
A party official told Reuters the congress could be held as soon as 21 May and would begin no later than 6 June, the first day of the Islamic holy month of Ramadan.
Among those tipped as successors to Mr Davutoglu are Transport Minister Binali Yildirim, who is close to Mr Erdogan, and Energy Minister Berat Albayrak, who is the president’s son in law.