Speaking to Football Insider, Bent said the left-back will be pushing for a move down South to be completed before the English transfer window closes on 8th of August.
He said: "He’s desperate to leave Celtic and join Arsenal in the Premier League, I’m sure of that.
“At the moment, it looks like it might be up in the air as Celtic want more money up front and Arsenal are reluctant to pay it.
“You can’t blame Tierney for wanting to join Arsenal.
"Celtic are a massive club but he has won everything there and proved himself in the SPL. He will want to show he can do it in the world’s biggest league, and at a higher level.”