The Russian club have been chasing the former Spartak Moscow forward for some time now, and were close to a £10.5 million deal with Spurs during the winter.
It was a time when Pavlyuchenko was out-of-favour at White Hart Lane, and had admitted to considering the possibility of a move away from the club.
However, the striker went on to put in strong performances during the second-half of the season, helping Spurs to a fourth-placed Premier League finish.
Pavlyuchenko has recently admitted that he would like to continue to ply his trade under manager Harry Redknapp, but The Daily Mail reports that Lokomotiv are intent on offering Odemwingie in part-exchange for the sought-after Russian.
But if Spurs are interested in chasing big name forwards during the transfer window, it has been speculated that the Russians will offload the Nigeria international to fund a move for Pavlyuchenko.
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