The 20-year-old spent the second half of last season on loan at Championship outfit Ipswich Town as he could not command a starting berth at Selhurst Park.
Swansea City are believed to be keen on signing the Welshman this summer, a possible move that has been given the approval of national boss Chris Coleman. However, Pulis has insisted that he wants Williams to remain with Palace and prove that he is good enough to regain his place.
He told the South London Press: "Jonny is a Crystal Palace player until deemed otherwise. He's one player that there is always going to be speculation about that he could be going – you are never going to take that out of the game.
"If people want to talk about it, then they will talk about it. But Jonny comes back at the same time as the rest of the players. It is his responsibility to come back and do as well as he possibly can to get back in the team.
"He is a great lad and has got the potential – that is the word to use. He has got to fulfil that potential."
Williams made nine substitute appearances last term, but did not start a Premier League game.