Davutoglu is in Tehran for high level talks with Iranian officials over a raft of issues, including the Islamic republic's controversial nuclear programme which world powers believe is masking a drive for atomic weapons.
Tehran denies the charge.
"Turkey is ready to act as an intermediary in the issue of uranium exchange as a third country and hopes to have a fruitful role in this," Davutoglu said at a joint media conference with his Iranian counterpart Manouchehr Mottaki.
"We will continue to try our best to see what we can do for this nuclear fuel swap."
Iran is at loggerheads with Western countries over a UN-drafted deal to supply high-grade uranium as fuel for a Tehran research reactor in return for the Islamic republic's low-enriched uranium.
The deal has, however, hit a deadlock as Iran insists that the exchange of the two materials take place simultaneously and inside the country, a condition rejected by the West.
Mottaki on Saturday said Iran was still ready for the deal and planned to hold talks with all 15 members of the UN Security Council, which includes Turkey, to break the deadlock over the deal.
Davutoglu said that Ankara believed that the "solution for Iran's nuclear programme is through negotiations and diplomatic process."
Turkey, a non-permanent member of the Security Council, has consistently resisted a US push for new sanctions against Iran in response to its nuclear programme.
