Swansea City have made an offer for Jones, 28, and Pulis says that it is up to the Trinidadian forward whether he stays or goes.
"There is an offer there and it's around about what the club would expect," said Pulis. "But I've said to the player 'if you don't want to leave mate, then you can stay', and he wants to stay.
"We are in no financial trouble at this football club. We run the club soundly and I'm honest with the players.
"If it comes to a point where we accept an offer from Swansea then it will be down to Kenwyne whether he wants to go on that. Because if he says no, there will be no problems with me."
Jones, whose current contract is due to expire in June 2014, has scored four goals in his last eight appearances for the Potters.