The meeting in İstanbul would be preceded by a visit to Moscow by a Turkish defense delegation this week, NTV television and CNN Turk cited Turkish presidential sources as saying.
Millions of tons of wheat and other grains are currently stuck in Ukrainian ports, either blockaded or occupied by Russian forces, and vessels face the danger of mines.
According to the Turkish foreign ministry, the UN has submitted a plan to facilitate exports that would see safe corridors set up around known mines.
The plan would not require lengthy and complex demining operations, Turkish Foreign Minister Mevlüt Çavuşoğlu said last week.
The initiative has been backed by the European Union but received a cautious response from Kyiv, which is looking for ways to export the grain by land, without talking to the Russians.
Çavuşoğlu this month hosted his Russian counterpart Sergei Lavrov in Ankara to discuss the issue, but without conclusive results.
The Turkish reports did not specify who would attend next week’s meeting.
Turkish President Recep Tayyip Erdogan discussed grain deliveries with UN Secretary-General Antonio Guterres on Monday.
Turkey is “exerting joint efforts with the United Nations for the export of Ukrainian grain via the Black Sea in a bid to avert a global food crisis,” Erdoğan’s office said on Tuesday.