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.
- Hearts strike late to stun Celtic
- Scottish Premiership Team of the Week
- Ntcham leaves Celtic after four years
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.
'An exciting move for Hart'
Sky Sports News' Michael Bridge:
"This is an exciting move for Joe Hart nearing the end of his career.
"Hart's future at Spurs looked bleak after the north London side signed Pierluigi Gollini on loan from Atalanta. Hart loves being at Tottenham but it's understood he wasn't in Nuno Espirito Santo's plans ahead of the new season. Alfie Whiteman has impressed in pre-season and is expected to be confirmed as Tottenham's third choice 'keeper.
"Hart featured in the Europa League and FA Cup last season but was never considered competition to captain Hugo Lloris.
"Despite rarely featuring, I'm told Hart was a highly regarded member of the squad and loved his time at the club.
"Hart is still in good condition but there will be concerns he's not played much over the past 12 months."
Follow the summer transfer window with Sky Sports
You can follow all the latest transfer news and rumours in our dedicated Transfer Centre blog on Sky Sports' digital platforms, as well as keeping track of all the developments on Sky Sports News.
New series: Football's Cult Heroes
Football's Cult Heroes is a brand new podcast series exploring the stories of the players that carried their clubs on their backs - on and off the pitch.
Told by the players, fans and journalists that were there, we delve into why these players created such a strong bond with their fans and how they are still remembered years on.
Follow on Spotify so you can listen to the weekly episodes as soon as they drop.