The News of the World says the Russians plan to lure the Israeli midfielder away from Anfield with a bumper pay deal.
Benayoun, 29, spent last week discussing his future with agent Ronen Katsav, despite having three years left on his contract.
But he insisted: "It's flattering other clubs want me but what is important is where I am now.
"I am enjoying myself and it's good for me here. In a few more weeks, it will be the right time to talk about certain things."