Hutton, who played for Tottenham and other teams in the top flight, has claimed that Harrison is tempted by a move to Newcastle United.
The Magpies sit in third place in the Premier League, and will look to strengthen their squad in the winter.
Hutton stated, per Chronicle Live: "I think if Newcastle come calling, somewhere that you can see what they are doing, they are trying to build something, you would definitely want to be a part of that.
"I think from a Leeds point of view, they are still in a position that they are on the edge. I do not think that they would want to get rid of a player like that, even though [Crysencio] Summerville has come in and done really well.
"I think it is healthy to have that competition, to have more than one player available for the position. When you are used to playing week in and week out and then you lose your spot, the only thing you want to do is get back playing.
"So it is probably something that he will be thinking about."