The Stoke winger - out of the Republic of Ireland's friendly against Argentina in Dublin tonight because of a groin strain - has now pledged his future to the Potteries side.
Hoops boss Neil Lennon first revealed his interest in the £2million-rated player two months ago and Lawrence publicly stated his desire to move to Parkhead.
As recently as the weekend he claimed the imminent £10million sale of international team-mate Aiden McGeady to Spartak Moscow would clear the way for Celtic to make a bid for him but now appears to have performed a U-turn.
"The idea of a move to Celtic was really appealing at the end of last season," he told the Scottish Sun.
"It has gone on for so long now and they have bought a lot of players.
"Clearly, they've had plenty of opportunity to come and get me but for whatever reason it hasn't happened.
"Stoke have been brilliant with me, stating they were prepared to give me the chance of a move if the conditions were right.
"I really wanted the opportunity to play for Celtic. If they had come in for me I would've been happy to go.
"With things dragging on it has given me time to reconsider everything.
"I have had a brilliant pre-season with Stoke, I've really enjoyed it, and now I feel I've got to be fair with them.
"I feel the best thing for me now is to stay and try to play in the Premier League."
Lawrence, 29, added: "Of course it's a big disappointment when a huge club like Celtic comes in for you and it looks like an exciting opportunity - but nothing materialises.
"Maybe it wouldn't have been the right opportunity. Now I'm just focusing on the new season with Stoke."