The 22-year-old, who scored 19 goals in 31 league starts this season, is widely expected to leave the club this summer.
And Boro boss Gordon Strachan has made the first move, according to the News of the World, putting a £2.5million on the table at Glanford Park.
Hooper, with 50 goals to his name in the last two seasons, has already been shown around Boro's Rockliffe Park training ground.
And Scunthorpe chairman Steve Wharton said: "There are four or five clubs showing an interest in Gary.
"I am not resigned to losing Gary this summer - but I would not be surprised if a transfer does happen."