The Hoops are keen on the 21-year-old midfielder and have been keeping an eye on his progress since last season. And they know Spurs are likely to allow their talent to leave permanently this summer.
Devine spent last term on loan at Preston North End who had first refusal on the player with a £6million future fee inserted into the initial loan agreement.
The Whites are believed to have looked to trigger that clause in his deal but, according to multiple reports down south, it came with a July 1 deadline which has now passed.
That has thrown the move to Deepdale for Devine into doubt and allowed Celtic to swoop back in should their hierarchy be able to do business. But the signing would also cost the Scottish Premiership champions £6m.
Read more
Celtic were worthy title winners but data points to a summer warning - Alan Morrison
Inside Shaun Maloney's key role in Celtic double: Tactics, Fotheringham & Osmand call
Wolves, despite relegation to the Championship last season, are reportedly also interested in Devine so there are a lot of moving parts for the midfielder to consider.
Devine is unlikely to be a part of Spurs' squad this campaign with the North London club snapping up Mateus Fernandes from West Ham while Sandro Tonali is close to a £100m switch from Newcastle United.
Players such as Lucas Bergvall and Rodrigo Bentancur, already ahead of Devine, will slip further down the order at Tottenham Hotspur Stadium.
So Roberto De Zerbi may be willing to part ways and bank a decent chunk of profit.
Martin O'Neill is said to be a fan of Devine.