Dembele has proven a revelation in Glasgow following his £500,000 switch from Fulham 18 months ago and has never hid from suggestions that he may use the Hoops as a stepping stone en route to bigger and better things.
And Hay is convinced that the French marksman is ready to make that step, but claims he would be happy enough to prolong his exit until the summer if necessary.
"I have a feeling he believes it is time to make the move but equally, if the right club does not emerge then I think he would be content to wait until the summer," he told The GET.
"I cannot see that he will be creating a fuss behind the scenes because he doesn’t come across as that type at all.
"Like most players who are confident of their own ability, I think he understands that if he is performing on the European stage and coming up with the goods then he will always remain on the radar of other clubs.
"I suspect, too, that if he is allowed to go in January that there will be a replacement lined up."