The 27-year-old appears to be on the way out of Arsenal, with his contract set to expire in summer 2025 and the English Premier League side are reluctant to trigger an extension.
Tierney made his long-awaited first team return against Crystal Palace in the Carabao Cup on Wednesday, lasting 69 minutes at left-back.
Manager Mikel Arteta was defiant on Friday that the Scotland defender remain in his plans, yet as the January transfer window approaches, speculation linking Tierney with a switch back to the Scottish Premiership continues to heat up.
It's believed that Celtic have been exploring options of a loan and a permanent transfer. But Sutton thinks the Hoops' chances of luring him to Glasgow's East End for a second spell could be blown out the water due to the financial packages other club's can offer.
“There’s already talk of Kieran Tierney coming back," the former Celtic striker wrote in his Daily Record column. "I can understand the excitement among fans. It would be a real feather in the cap if they can persuade him to return.
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“Tierney is a quality player – if he’s fully fit. That’s the big question after the last few years. I also have other reasons to be sceptical over the move. Finances for one. I can’t say I know him that well but it doesn’t seem that he is overly money orientated.
“That could be good news for Celtic. But there is absolutely no doubt there will be interest in him from clubs in England and abroad – and figures that can blow Celtic out of the water.
“It might become a heart over head job at that point for the player but if you were advising him, would another two or three year deal on big money somewhere not make more sense than taking a substantial pay cut now? Only he can answer that one.
"Even taking a slash in wages, it would still mean Celtic taking a serious deviation from their financial model. It would be a lot of money for not a lot of sell on value.
"Some players are worth it – and Tierney could be one of them. It goes back to the fitness issue though. He’s had a torrid couple of years and needs to be back playing regularly. It’s a gamble English teams can afford to take, but would Celtic? It’s a big question – and there are others around Greg Taylor and Alex Valle.
"I know I have been critical of Taylor at the Champions League level but he’s been a brilliant signing for Celtic. Ideally he’d sign a new deal but that now looks unlikely. Valle might fancy cracking it at Barcelona as there’s no sign of a permanent deal at Celtic in the pipeline. Tierney could be the answer to all of the above. I’ll not be holding my breath."