The Manchester United legend had talks with the Scottish Premiership giants over succeeding Neil Lennon permanently, but he fears that he has now been overlooked for the job.
Keane had hoped to get a shot at his dream appointment, but has told his friends that he feels the chance has gone.
Former Celtic manager Martin O’Neill had backed the 49-year-old for the job, but his chances are now fading fast following Howe’s interview with the Parkhead outfit.
Rangers legend Graeme Souness also believes that Keane would be the perfect man for the Hoops job, and while some within the Celtic hierarchy love his passion, others prefer a more modern coach.
The Premiership powerhouse want the Scottish top-flight title back next season after Rangers pipped them to it a couple of weeks ago, and they want a manager who can hit the ground running and deliver immediately.
Keane once managed Sunderland and Ipswich Town and was O’Neill’s assistant with the Republic of Ireland before taking up a similar position at Aston Villa and Nottingham Forest.
While appointing the former Celtic midfielder as Hoops boss would be box office for Scottish football, going for the more experienced and tried-and-trusted Howe seems like the more reasonable thing to do.
The former Bournemouth manager proved himself in the Premier League before taking a deserved break last term after the Cherries relegated, and Celtic could do with his style of football and technical know-how for the tasks ahead.