That’s the opinion of his former team-mate Scott Brown.
Arsenal forked out £25million for Tierney on transfer deadline day after spending the summer pursuing the star.
Unai Emery was desperate to improve his defensive options at the Emirates, having seen his side ship 51 Premier League goals last season.
The Gunners were poor at the back last year, and Emery went into the summer transfer window looking to bolster his squad with the signing of 22-year-old Tierney.
Arsenal had two bids turned down by Celtic, with Neil Lennon’s side keen to ensure they received the £25m up front, with the North London side offering it in instalments.
In the end, Arsenal got their man after paying an undisclosed fee, but Brown warned that Tierney may not be in London for long.
Speaking on Monday, he suggested that if the star impresses, he could follow in the footsteps of players like Cesc Fabregas and Thomas Vermalen in signing for Barcelona.
“You don’t know what could happen,” he told The Herald.
“He could have a fantastic couple of seasons and end up at Barcelona or PSG or wherever.”
Brown was complimentary of Tierney and praised his efforts at Parkhead, while telling his replacement Boli Bolingoli that he needs to push on and fill his boots.
“There are pictures on the wall all over the club of players who have left, and everyone would wish them all the best,” he said.
“They can come back as well, that’s what this club is all about.
“I see Ajax bringing players through and selling them on – and they have a party for them leaving.
“We try and criticise. It’s a different level.
“We wish him all the best. We just concentrate on now and [new left-back Boli Bolingoli] has to push on and try to get to the levels that Kieran did.”