Lawrence believes he has no longer has a future with the Potters and is desperate to join the Hoops this summer.
Celtic have reportedly bid £1.5million for the 28-year-old, who said in the Stoke Sentinel: "Celtic are a massive club and I just hope Stoke and Celtic can come to an amicable agreement for me.
"I hope I don't get priced out of a move. If Stoke are looking for £2million, that sounds about right - and will be a good deal because I only cost £500,000.
"My agent says there could be another couple of clubs interested, but I've said to him I'd love to go to Celtic because I don't think there's a bigger club for me.
"I know Celtic haven't had the best of seasons, but if they can bring in a few players, then I'm sure we can try to and turn things round up there."
Lawrence revealed he had discussed the prospect of joining Celtic with Republic of Ireland team-mate Robbie Keane, who spent the second half of last season on loan at Parkhead.
Lawrence said: "Keano says it's an absolutely massive club with unbelievable support, stadium and training ground. He rates it as one of the biggest clubs in Britain and I'm very excited about the prospect.
"I'd love playing in front of 60,000 fans; it's already something I've done and enjoyed with Ireland and Stoke this season.
"Playing in the Champions League would also be something special. But I think qualifying starts when I'm supposed to be on holiday, so I don't think the missus will be too happy."
Source: Team Talk
Source: Team Talk