French side Lyon, now managed by former boss Gerard Houllier, are interested in signing Baros in an £8m deal but the player is not keen to play under Houllier again and would prefer to remain a Red.
Baros' agent Dalibor Lacina said: "Milan's decision has been made easier by the fact that Liverpool are playing in the Champions League.
"This is not a decision against Lyon - this is a decision for Liverpool."
Despite wanting to stay Baros may find himself forced out if Liverpool do sign Dirk Kuyt or Peter Crouch.