"My agent told me there was some interest about a week ago and I think the clubs have just been getting on with it and speaking to each other ever since," explained Lawrence.
"As soon as the manager's position is made clear I would have thought they would get nearer to agreeing a fee.
"I'm just waiting to see what happens with the manager. I don't think anything will be getting done until his situation is resolved."
Lennon appears to have made strengthening his midfield one of his priorities and Celtic remain favourites to sign the out-of-contract Wales international Joe Ledley from Cardiff City.
Ledley, who is also interesting Rangers, Everton, West Ham United, Blackburn Rovers and Wigan Athletic, visited Celtic's training ground on Monday but is to travel to meet officials of Italian Serie A outfit Roma early next week as he considers his options.
Celtic last month missed out on the signing of Republic of Ireland midfielder Steven Reid, who opted to join West Brom after being released by Blackburn.
Lawrence revealed he had discussed the prospect of joining Celtic with international team-mate Robbie Keane, who spent the second half of last season on loan in Glasgow.
"I asked Robbie Keane (about Celtic) last week when I was away with Ireland and he said it was a massive, massive club, with an amazing support and fantastic training facilities," he said.
"I think Celtic need to do well next season, there's a little bit of pressure to win something.
"And if I did get the chance I'd be trying my best to help them do that."
The Nottinghamshire-born Lawrence, who has also been the subject of interest from Wolves, began his career with Mansfield Town before a three-year spell with Sunderland.
He had initially joined the Potters on loan from Sunderland, where he played under present Wolves manager Mick McCarthy, and the move was made permanent for a fee of £500,000 in January 2007.
Lawrence became a first-team regular under Tony Pulis and signed a new contract last year that tied him to the club until 2013.
However, only 14 of his 33 appearances this season came as part of the starting line-up.
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