Wagner said on Jan 11 it had captured Soledar, and Russian-installed authorities in Ukraine's eastern Donetsk region said earlier this week they were in control of the salt-mining town, where intense fighting has taken place.
The RIA FAN website - part of Prigozhin's media holdings - quoted a Wagner commander as saying the mercenary company would send the bodies from Soledar to Ukrainian-held territory in four or five convoys totalling about 20 trucks.
Saturday's report did not say how many bodies would be returned to Ukrainian authorities, but said Ukraine's forces had suffered heavy losses in Soledar.
It said Prigozhin had made clear that soldiers' bodies should be returned to Ukraine in a "dignified" way, but gave no further details about the planned operation.
Ukrainian authorities said during the fight for Soledar that Russian forces sustained heavy losses.
Prigozhin, who previously shunned the public spotlight and denied connections to Wagner, admitted in September that he founded the mercenary army, which has played a major role in the conflict. He has described Wagner as a fully independent force with its own aircraft, tanks, rockets and artillery.