It was reported yesterday to be on a short list of two for a similar position at the London club. However, sources in the English capital last night insisted Lawwell had been offered the job after a meeting in the city on Friday, says The Herald.
Lawwell, who took over from Ian McLeod at Celtic in 2003, turned the offer down.
Dr John Reid, the Celtic chairman, issued a statement last night assuring fans that the successful chief executive would be staying at the club.
"Peter is a valuable and highly valued part of Celtic Football Club and remains so. Peter will continue to work with everyone at Celtic to ensure that the club enjoys even more success and maintains its pre-eminent position within Scottish football," the statement said.