The Hoops chief has been linked with a job with the Premier League side.
Celtic chief executive Peter Lawwell has issued a cagey response after being asked about whether he would soon be following Ronny Deila out of Parkhead, but conceded that he will not be with the Hoops forever, the Daily Mail reports.
The Daily Mail reported last month that Lawwell was included on a shortlist of candidates that Sunderland were looking at to replace Margaret Byrne. And while he suggested that he is solely concentrating on finding the man that will add to the Bhoys' five Scottish Premiership titles in a row, he hinted that a move away from the club that he has been with since 2003 could be possible.
"But, at the moment, my only focus is on getting a new manager, getting him in and being stable.
"Then we will see."
The Mail's report in April suggested that he was attracting interest from England due to his ability to balance the finances at Parkhead while also ensuring that the club's form on the pitch was also strong.
And while a move to the Stadium of Light may see his side win fewer trophies, he may have a similar opinion about a move south of the border to several of the players that have left the Hoops in recent seasons for the Premier League or Championship.
The likes of Virgil van Dijk, Victor Wanyama and Gary Hooper have all departed in recent seasons despite joining clubs which have much slimmer chances of winning silverware and reaching the Champions League.
And if Lawwell sees a potential switch in a similar way then Celtic's summer may involve finding a new chief executive, as well as a new manager and working on building a squad capable of securing a sixth league crown in a row.