Joe Hart is expected to undergo a medical with Celtic on Tuesday ahead of a move from Tottenham.
Sky Sports News reported Celtic's interest in the former England goalkeeper last week, but talks had reached an impasse by the weekend.
But after constructive talks on Monday, Hart is due in Scotland to complete a switch to Parkhead.
The 34-year-old, who has had previous spells at Manchester City, West Ham and Burnley, has one year left on his contract at Spurs.
Tottenham have since brought in Italian goalkeeper Pierluigi Gollini from Atalanta to compete with Hugo Lloris.
Celtic, who were knocked out in the qualifying rounds of the Champions League last Wednesday, also had an interest in Watford goalkeeper Ben Foster.
Tottenham are willing to sell a number of their first-team players this summer in order to help fund their rebuild of the squad, with players such as Serge Aurier and Moussa Sissoko potentially leaving.
Toby Alderweireld, Erik Lamela and Juan Foyth have already been sold to help fund the arrivals of Gollini and Sevilla winger Bryan Gil.