The experienced striker worked with Harry Redknapp at Southampton, Portsmouth and Tottenham Hotspur, and the Hoops boss has admitted his interest in linking up with the former England international once more at Loftus Road.
Pulis has claimed that Crouch will decide his own future, hinting that the Potters would be willing to sell if a suitable bid is lodged and a replacement can be recruited before the close of the transfer window.
"I've spoken to Peter about it and it is up to him whether he wants to go," said the Stoke manager.
"He's very happy here and he's made that clear. It's got to be right for us but we'll need someone to come in and do the same job."
Crouch cost Stoke £15m when he arrived from Spurs in the summer of 2011.