Last season, the Tigers suffered relegation from the top flight after just one year back among English football's elite, but Clucas was one of their most consistent performers and he scored three times in 37 league appearances.
However, according to the Daily Mail, his form has attracted the attention of four teams, with Newcastle United, Leicester City, Burnley and West Bromwich Albion all said to be interested in his signature.
Each club is looking to strengthen their squad ahead of the upcoming campaign, and the possibility of signing homegrown player Clucas will appeal.
Since moving to the KCOM Stadium in 2015, he has scored nine times in 93 matches in all competitions, and it has been suggested that he would cost as much as £10m this summer.
The 26-year-old still has two years remaining on his contract at Hull.