The former Manchester United star has distanced himself from the speculation.
He said: "Be very surprised if you see me walking through the gates at Celtic Park - except if it's for the Old Firm game on Tuesday week because I might come up for that one."
Keane believes Neil Lennon is doing a fine job as interim boss at Celtic Park, even though the Hoops were recently knocked out of the Active Nation Scottish Cup semi-final by Irn-Bru First Division side Ross County.
He said: "Celtic are a bigger club than anyone will ever understand unless they have been involved there.
"I was there for six months and I had my problems with a few injuries, plus the manager didn't really pick me. The sheer size of the club is staggering. Neil has made that point and I couldn't agree more. Hopefully they will get the right manager and I have to say Lenny is doing well.
"He's won four league games but I know they lost in the Scottish Cup. They're having disappointments but that's when you find out who the real supporters are."