Pavlyuchenko, 27, is desperate to leave in January and Roma sent director Daniele Prade to London this week to open talks.
But Redknapp warned: "That would be up to the chairman but he's not a player we want to lose.
"He wants to play regularly but it's been difficult because the other strikers have all been great. There has been talk about him having to move to get games but we are happy with him.
"If he's not happy and somebody wants to pay the right money for him then something might happen. But he won't be leaving here cheaply."