O'Shea, a former Manchester United teammate of Keane's, is now working with the Republic of Ireland assistant coach.
"His appetite since he's come into this job will have increased.
"He's obviously learned from Martin (O'Neill) along the way, too. He'll relish the challenge. If it does happen, Celtic will be getting a very hungry and determined manager."
Asked if he thought that would be the outcome, he added: "Yeah, it looks very much like it now.
"It was mentioned at the start of the week and slowly but surely it's snowballed into having talks with Celtic. So I'd very surprised if it doesn't get across the line."
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