The move comes after talks between Davutoglu`s Justice and Development (AK) Party and the second-placed Republican People`s Party (CHP) ended without agreement last week.
Davutoglu was due to hold talks with MHP leader Devlet Bahceli at 2: 00 p.m. local time (GMT 1100) at the Turkish parliament.
According to the prime ministry sources, Davutoglu will "talk with Bahceli without any prejudice".
Davutoglu is expected to highlight alternatives, including the formation of a government within joint and agreed issues.
Turkish media has reported the MHP has four conditions on joining an AK Party-led coalition: no changes to the principles enshrined in the constitution; an end to peace talks with Kurdish separatists; the reopening of corruption investigations that have targeted figures close to the AK Party; and a guarantee of the country`s parliamentary system.
Haluk Alkan, a political analyst the Ankara-based Institute of Strategic Thinking, said the MHP`s conditions could limit the likelihood of a coalition being formed.
"In terms of forging a coalition government between the AK Party and the MHP, it is a significant advantage that the two parties` electoral bases are very close to each other," he told Anadolu Agency.
"However, they need to sit at the table without preconditions and negotiate over the principles of a joint government program. If the MHP tables conditions that the AK Party is not sympathetic towards, then this attitude will eliminate any possibility of a government."
Davutoglu requested the meeting with Bahceli following the failed talks between the AK Party and the CHP. The pair met a week after the June 7 election but Davutoglu told reporters the MHP had opted not to take part in government.
Together, the AK Party and the MHP hold more than two-thirds of parliamentary seats. - Ankara
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