Lawrence joined Stoke for £500,000 from Sunderland in January 2007 after initially joining on loan in November and he has gone on to make 125 appearances for the club, scoring 24 goals.
The Republic of Ireland international was named the club's player of the season after their promotion campaign from the Championship in 2008/09, but he has been less involved in the Premier League.
He started just 14 league games last season and has said he would walk to Glasgow to seal a move to Celtic. The Bhoys have already failed with a £1.5million bid for the 28-year-old but an offer of around £2million should secure his services.
However should Lawrence remain at the Britannia Stadium, Pulis would be more than happy.
"I've never wanted Liam to leave," said Pulis in the Stoke Sentinel, "and if he doesn't, then I'll be very happy to have him here when we all report back next month.
"He's been one of the best signings this football club has made because he's played a massive part in what we've tried to achieve here over the last few years.
"And he's got better and better as a player, getting himself into the Ireland team and scoring goals for them."
Pulis has no problems with Lawrence's desire to move on, however, after failing to nail down a regular spot in the Potters' midfield.
"He wants to play week in, week out... that's Liam," Pulis added. "But I've got no problem with that kind of hunger and fully respect him for that."
Source: Team Talk
Source: Team Talk