The United States and the European Union have called on Moscow to release the sailors who are being held in pre-trial detention after Russia seized three Ukrainian navy vessels and their combined crew in November.
Russia said the vessels entered Russian waters illegally. Ukraine has said the two small gunboats and tugboat were captured illegally and accused Russia of military aggression.
The unnamed diplomatic source was quoted by Izvestia as saying the sailors would have be put on trial in Russia before any swap deal were made, but that there were many Russians being held in Ukraine who could be exchanged.
No date has been set for the sailors' trial. The Ukrainian sailors in custody have said they consider themselves prisoners of war, a status rejected by Moscow.