Thompson has attracted interest from several Football League clubs, but Scunthorpe appear clear favourites for his signature.
"I have no doubt that he will make the step up in League One," McIllroy, whose assistant is the former Iron No2 Mark Lillis, told the Morecambe Visitor.
"He is a big, strong boy and is a match-winner. He is in the prime of his career and can kick on and flourish.
"I think we have lost him. That is disappointing but I wish him all the best.
"He has done a great job for me and he has enjoyed it here. Now I am looking forward to seeing how his career progresses."
Thompson netted eight goals for the Shrimps in League Two this season, and created 11 strikes - more than anyone else in the division.