The newspaper, using reports from Belarus, where the tournament is being played, said Ovechkin did not confirm he would play Thursday against France.
Ovechkin was injured Sunday in a preliminary-round game against Germany. He had an MRI exam on his right knee which did not show ligament damage, and the Capitals released a statement saying he would be completely healthy in time for NHL training camp and the 2014-15 season. The statement did say the injury requires rest.
According to the Post report, Ovechkin did not wear a brace on the knee at practice.
If Russia, which was 7-0 (21 points) in the preliminary round, defeats France, it would next play either Sweden or Belarus on Sunday in the semifinals.
Ovechkin had three goals and six assists in six games.