Kieran Tierney will sign a five-year deal at Arsenal if his proposed £25m transfer from Celtic goes ahead.
The Premier League club already had two bids for the left-back rejected but a Scottish record deal has been struck for the 22-year-old.
Tierney will undergo and medical and discuss personal terms, with the English top-flight transfer window closing at 17:00 BST on Thursday.
The Scotland international last played for Celtic on 4 May due to injury.
Speaking immediately after Celtic's 1-1 draw away to Cluj in Champions League qualifying, manager Neil Lennon said: "I don't know anything. I've said the last few days it wouldn't surprise me [if Arsenal came back in for the player].
"If he goes, he goes with everyone's best wishes. He's an outstanding talent and a great kid."
Tierney, who has been restricted to just nine appearances this year and had a summer double hernia operation, has won four league titles with Celtic and has been on the winning side for two Scottish Cups and two League Cups.
Celtic captain Scott Brown echoed the sentiments of his manager in Romania, adding: "Kieran's a fantastic player. There's always going to be interest in him. He will be a big miss if he goes."
'This could be very good for him' - analysis
BBC Scotland chief sports writer Tom English
It's the right age and the right time for Celtic and Kieran Tierney. He's won everything he can at Celtic outside of Europe and he's going to Arsenal to try and do something in Europe, the Premier League, advance his career, stake his claim for that Scotland left-back spot.
He just needs to get fit and try to put his best foot forward. This could be very good for him.