The Republic of Ireland international started only 14 games in the 2009/10 season and found himself behind Dean Whitehead and Rory Delap in the pecking order.
Lawrence, 28, told the Sentinel: "I don't want to leave Stoke but it is becoming increasingly difficult with other players playing in my position.
"I have nothing but respect for (manager) Tony Pulis and have never fallen out with him in three and a half years at the club.
"But, purely for footballing reasons, it is time to move on. That is best for both parties.
"The team has done well whether I have played or not, so I am not going to moan and say I should be playing. But I am not a player who is happy to sit on the bench and just pick my wages up.
"I have agreed with the manager that this is the right thing to do. He told me he didn't want me to go but he understood where I was coming from."
Lawrence joined Stoke for £500,000 from Sunderland in January 2007 and played a major role in their promotion to the Premier League the following summer.
He signed a new four-year deal at the Britannia Stadium last summer but things have not worked out how he had hoped.
Lawrence has been linked with a move to Wolves, which would see him reunited with Mick McCarthy, his former boss at Sunderland.
He continued: "I am aware of interest from clubs and hope I can stay in the Premier League but I won't be doing anything without Stoke knowing."
Source: Team Talk
Source: Team Talk