Shrews boss Sam Rickett has revealed he offered Hart the chance to return to his hometown club, where he began his professional career 16 years ago.
Ricketts said: “In terms of interest, from our part yes. Joe would have an interest, but not so much as in coming back to play.
“He's still at a level where he can play at a much higher level, not just in this country but abroad as well.
“It's something that I put to him and his people, I said 'do you fancy coming back?'. But he's ready to continue his career at the highest possible level.
“He has interest from top-level teams so it's not going to be one for us. Sentiment doesn't rule the head on this one."