Keane held informal talks with the Glasgow club over the vacant manager’s job after an approach by Celtic owner, Dermot Desmond.
Celtic chief executive Peter Lawwell has confirmed the club are interested in appointing Keane, but says the Republic of Ireland assistant manager faces competition from as many as nine other rivals, with Henrik Larsson, Malky Mackay, David Moyes, Owen Coyle and Jackie McNamara also believed to be in the frame.
Former Celtic and Ireland keeper Bonner believes Keane could do with a little more time learning under Martin O’Neill before taking on the Parkhead role.
“I think it’s a stepping stone for Roy to become the main man again as a manager but what a great opportunity for him with the Irish team,” Bonner told RTÉ Radio.
“We all felt that when he went in there, that it’s a learning process to be in under someone like Martin. And maybe that’s somewhere where Roy… you know he’s a young man coming out of football going into management and you have to have a transition.
“He did quite well at Sunderland, failed a little bit in the other jobs and it’s a learning process. I think it’s a year too early for him but in saying that, if the job comes up at Celtic, I don’t think he could knock it back.”
Bonner’s old Irish team-mate Ronnie Whelan admits he will be disappointed if Keane takes the Celtic role.
The ex-Liverpool star told Today FM: “It’s Roy’s decision. I think plenty of us were surprised he went into the job with Martin O’Neill in the first place. “We’d be a little bit disappointed if he didn’t see it through a bit longer than this.”