Sunderland AFC News: Celtic chief executive discusses move, Watford boss to go after Cats clash
Lawwell was the subject of speculation over the chief executive vacancy at Sunderland last month after the resignation of Margaret Byrne.
With Sunderland's Premier League status now assured, Ellis Short will step up his attempts to land a successor to Byrne, who can handle the day-to-day running of the club.
And when asked about the Sunderland speculation in an interview with the Scottish Daily Mail, Lawwell appears have hinted at a Celtic exit after he appoints a successor to departing manager Ronny Deila.
"Listen, we are at Five-in-a-Row (five league titles) we are in a good place. I won't be here forever, put it that way," he said.
"But, at the moment, my only focus is on getting a new manager, getting him in and being stable.
"Then we will see."
There will definitely be a departure from Sunday's opponents Watford this summer after the Hornets confirmed that the Sunderland clash will be the last game at the helm for manager Quique Sanchez-Flores.
The Spaniard has been the subject of speculation for several weeks and Watford today released a statement rubber-stamping his exit.
Meanwhile, Sunderland striker Jermain Defoe has been discussing his hopes of a place in the England squad for the summer's European Championships.
Defoe has netted 15 Premier League goals this season, with Jamie Vardy and Harry Kane the only Englishmen to have scored more top flight goals.
"If I do go, it will be a dream because I still feel like I can score goals for England," said Defoe.