The premier has this week met all three of Turkey's opposition parties after his ruling Justice and Development Party (AKP) failed in June 7 polls to win an overall majority for the first time since it came to power in 2002.
Davutoglu on Wednesday met the leaders of the pro-Kurdish Peoples' Democratic Party (HDP), the first time a pro-Kurdish party has been involved in coalition talks in Turkey.
"An alliance in a coalition with with the HDP does not seem to be on the agenda," Davutoglu told reporters after the meeting with HDP co-chiefs Selahattin Demirtas and Figen Yuksekdag.
The premier had on Monday met officials from the second-placed Republican People's Party (CHP), which did not rule out taking part in a coalition with the AKP while insisting on several conditions.
However officials from the Nationalist Movement Party (MHP), who he met Tuesday, refused to enter a coalition with the AKP.
Analysts say a so-called "grand coalition" between the AKP and CHP could be viable but still faces numerous stumbling blocks, in particular over the role of strongman President Recep Tayyip Erdogan.
Signup to our newsletter and follow us on Facebook and Twitter!
Davutoglu has 45 days to agree a coalition and if he fails to do so Erdogan has the right to call snap new elections.
Further coalition talks are expected next week after several days of holiday in Turkey marking the holy Muslim month of Ramadan.
"The only viable coalition option still seems to be an AKP and CHP coalition," said Ozgur Altug at BGC partners in Istanbul in a note to clients after the latest talks.
"If this is not the case, elections might be repeated."
The HDP scored a huge breakthrough in the elections, taking 80 seats, as many as the MHP. The sheer fact of a Kurdish party holding coalition talks with the premier would have been unthinkable a few years ago.
Critics accuse the party of being the political shop window of the Kurdistan Workers' Party (PKK) which has fought a deadly insurgency in the southeast against the Turkish state for decades.
Davutoglu called on the HDP to be "reasonable" and adopt a "clear and transparent position against violence."