Pavlyuchenko had been expected to leave Spurs during the January transfer window, but in the end it was Robbie Keane who left for Celtic to make way for loan signing Eidur Gudjohnsen.
Pavlyuchenko, though, is thought to remain unhappy about his lack of first-team opportunities at White Hart Lane and, with Russian clubs still able to buy players until mid-March, Lokomotiv are said to have made a £10.8 million bid this week.
However, the club's president, Nikolai Naumov, has said Redknapp was not willing to allow the player to leave until the end of the season.
"It's our understanding that the view within Tottenham is split," he said in the Daily Mail. "The directors have no objection to selling the player, but the coach wants to keep him until at least the summer. We'll take about the transfer at the end of the season."