The 23-year-old has been a key figure for the Black Cats this term as they strive for promotion to the Premier League, netting 15 goals and providing four assists in 33 Championship matches.
Clarke produced one of his trademark finishes past Birmingham City John Ruddy on Saturday to give Sunderland a first-half lead in the Second City, however the visitors went on to lose the match.
The defeat at St Andrew's @ Knighthead Park cost Michael Beale his job, with Mike Dodds set to run the first team on an interim basis until the end of the season.
According to Football Insider, Sunderland are expecting a tough battle to retain the services of Clarke past the conclusion of the 2023-24 term.
The report claims that the attacker's future at the Stadium of Light will be determined largely on whether the Black Cats can secure promotion to the Premier League this season.
After a sixth-placed finish last campaign under the experienced watch of Tony Mowbray, Sunderland are currently 10th in the Championship standings, seven points adrift of sixth-placed Hull City.
It is understood that Premier League outfits Burnley, West Ham and Brentford have all shown an interest in Clarke since the start of the term.
Vincent Kompany's Clarets supposedly submitted a formal bid for the former Tottenham Hotspur man ahead of the 2023-24 campaign, although it was swiftly rejected by the Black Cats.
It is also understood that Serie A side Lazio offered £14m for Clarke during the January transfer window, but again the North-East club rebuffed the advances of a top-flight side.
With the winger's current terms at the Stadium of Light expiring in June 2026, Sunderland are in no immediate danger of losing the player for cheap.
As well as Thomas Frank's Bees and David Moyes's Hammers, it is also stated that a number of other Premier League teams are considering a move for Clarke ahead of the 2024-25 season.
Due the return of Amad Diallo to parent club Manchester United and Patrick Roberts's injury issues, Clarke has burdened the vast majority of goalscoring responsibility for Sunderland this term, netting three times more than any of his teammates in the Championship.