The former Hearts and Scotland keeper has been without a club since leaving Sunderland two years ago and has been plagued by a series of injuries in recent years.
He could become Ronny Deila's first signing as Hoops boss after being offered a Parkhead deal.
It would be a huge step in the right direction for one of Scotland's finest shot-stoppers.
And former Celtic keeper Rough has tipped Gordon to complete his recovery and challenge Fraser Forster for the No.1 jersey this term.
Rough said: "Craig's got quality. At one point he was Scotland's goalkeeper and challenging Jim Leighton's records. I hope he does get back to where he was because he was a fantastic goalkeeper.
"I'm sure going to Celtic can get him back to where he wants to be.
"Of course Craig can do it. It's a long time for any player to be out of the game, never mind a keeper, so it would be remarkable for him.
"I don't know of a keeper who has been out of the game for two years and returned to the top.
"But I'm sure Craig has all the ability in the world to do it."
He went on: "I think Craig has got the capability to challenge Forster for the No.1 jersey. He can get back to where he was.
"Craig was top man when he was playing. The £9million price tag he had when he moved to Sunderland said it all - and I don't think he was anywhere near his peak when he went there.
"There was still a lot to come from him. I think he'll have a lot to prove, he'll want to prove to everyone that he can get back to where he was ... and that's a good thing."
While Gordon is edging nearer to a Celtic contract, new boss Deila will be determined not to lose his current first choice keeper this summer.
Forster will return home from the World Cup this week and interest in his services is likely to be high after another fine campaign.
Back-up goalie Lukasz Zaluska is heading for the Parkhead exit door after struggling for match action in the last few seasons.
The arrival of Gordon would give Forster some real competition should he stay at the club next term.
And Rough reckons the presence of the 31-year-old could be just what the England star needs.
He said: "I think he (Forster) does need that challenge. Everyone's saying that Fraser Forster's moving on, but as yet there haven't been any clubs attached to him.
"They maybe think there's going to be clubs coming in for him.
"If the two of them are there for the new season then it will certainly give Forster a shake.
"If Craig gets back to where he was then he'll most definitely be challenging.
"Forster must be thinking that he's tasted the World Cup, he's tasted being out with all these big, big stars in England, telling him what life's like down south, and he'll just have to make his own mind up."