That is according to former Scotland international James McFadden, who says the left-back is “Celtic mad” and is in no rush to leave Parkhead.
The Gunners have had a £15m bid for Tierney rejected by the Scottish champions but are expected to return with an improved offer for the 22-year-old.
The Premier League outfit have also been rumoured to have offered four of their young stars in part exchange for Tierney.
Offering Carl Jenkinson, Jordi Osei-Tutu, Emile Smith Rowe or Eddie Nketiah could not tempt Celtic into agreeing to sell.
Celtic though are thought to be open to a deal for Tierney – but only if the price is right.
There is optimism that an agreement will be reached between the two clubs, and personal terms are not expected to be a stumbling block.
McFadden thinks that the defender is ready to make the move south of the border but insists that he is worth much more than £15m in today’s market.
“[Virgil] van Dijk moves down for £13m plus his sell-on clause then goes for £75m. I think Kieran Tierney’s certainly at that level,” he said.
“Kieran Tierney is Celtic daft, so it’ll take something phenomenal for him to consider it”
“We’re not talking about him going to a smaller side to build himself up. It’s one of the top sides in England coming and saying we’re going to take your best player for a pittance.
“Kieran Tierney is Celtic daft, so it’ll take something phenomenal for him to consider it, and also for Celtic to consider it.
“I think it would need to take someone who’s going to compete for a title in England or go and try to win the Champions League for Kieran Tierney to leave, because he’s winning trophies, he’s playing in Europe, he’s playing for the club he loves.
“I think it would have to be something really special, and Arsenal at the minute won’t challenge for the title. They might further down the line if they can invest in their squad, but £100m is nothing in England.
“I don’t think Arsenal will blow him away and make him think ‘I have to go and sign for Arsenal’.
“Arsenal look like they’re trying to do things on the cheap, and if it’s £15m it proves they’re trying to sign as many players as they can for as little as possible.
“It tells you that they’re not ready to challenge for the title, and that’s maybe in the back of Kieran Tierney’s mind to say ‘Why do I just want to go and try to finish sixth or break into the top four, when I could be winning titles for the club I love?’”
It remains to be seen whether Arsenal come back with an improved offer for Tierney in the coming days.