Under the terms of the constitution, Erdogan could dissolve Davutoglu's caretaker cabinet and call for the formation of an interim power-sharing government to lead Turkey to a new election in the autumn, if no deal is reached by Aug. 23.
Such a temporary arrangement would theoretically hand cabinet positions to four parties with deep ideological divisions, leaving policy-making paralyzed and deepening instability which has sent the lira to a series of record lows, according to a Tuesday report by Reuters.
The currency hit a new low of 2.8776 against the dollar overnight.
The ruling AK Party failed to hold on to its majority in a June 7 election, leaving it unable to govern alone for the first time since coming to power in 2002. That plunged Turkey into uncertainty not seen since the fragile coalitions of the 1990s.
Davutoglu met with the leader of the right-wing opposition Nationalist Movement Party (MHP) on Monday in a last-ditch effort to agree a working government, but the nationalist leader refused all of the options he presented.
"After yesterday's talks, no coalition option remains for the party. Davutoglu will therefore return the mandate to the president this evening," the official told Reuters, asking not to be named because of the sensitivity of the situation.
Talks with the main opposition Republican People's Party (CHP) broke down last week, while parliament's fourth party, the pro-Kurdish Peoples' Democratic Party (HDP), has all along ruled out any coalition with the AKP.
Senior AKP officials had been betting that the nationalists, virulently opposed to greater Kurdish political power, would do anything possible to avoid a scenario in which the HDP would hold cabinet seats, even temporarily.
But nationalist leader Devlet Bahceli appears to be on a war footing, calculating that seeing Kurdish politicians in ministerial positions will so enrage those on Turkey's political right that they will flock to his support at the next election.
Erdogan could theoretically now hand the mandate to form the next government to CHP, Turkey's second biggest party, although it is also highly unlikely to be able to agree a working coalition before the Aug. 23 deadline.
Parliament could also vote to allow the current cabinet to continue working until a new election, but the MHP has already said it would vote against such a move and other opposition parties have little incentive to do any different.