The homegrown midfielder is not one who the club want to retain for the long-term.
Despite Gallagher being valuable to manager Mauricio Pochettino, he has value to the club from a financial perspective.
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If he is sold, the club can put all the funds received as profits on the books, allowing them to spend more on new transfers.
Speaking to talkSPORT, Cole said: Conor Gallagher can't leave. I know there are issues financially but Conor Gallagher has been brilliant, from start to finish.
Everyone has turned up in the last few weeks but Conor, you see a great player when he is playing in a struggling team.
Conor was still there, captain as well. I think it is imperative that the club keeps him."