The Gunners have had bids rejected for the Celtic left-back, but they are expected to make a late move for the Scotland international.
Celtic are adamant that they will not sell him for anything less than £25 million, and it seems the Bhoys have already lined up a potential replacement.
According to reports from The Scottish Sun, the Hoops are monitoring the 22-year-old who has been valued at around £7 million by his club.
The attacking full-back is a highly rated young talent and he was heavily praised by Dean Smith, who is now the manager of Aston Villa, a few years back when he was in charge of Wallsall.
“I can honestly say there was never any risk in my mind with Rico,” he told BBC Sport. “He was 16 when I threw him in against Leeds in a pre-season friendly. And he’s a quick learner. You give him a bit of information and he takes it on board.
“He fully deserves the award as he’s been excellent. If I were to liken him to anyone it would be a young Ashley Cole. And it’s up to him how far he can now go in the game. I’ve recommended him a couple of times to the England Under-19s because, if there’s a better left-sided player in the country at 18 years of age, I’d like to see them.”
Henry can play as a left-back and also as a winger, and he would be a terrific signing for the Bhoys.
However, it remains to be seen whether Celtic will make a move for him even if they don’t lose Tierney this summer.