Several companies suspended betting on the Republic of Ireland No.2 succeeding Neil Lennon.
Keane had started the day as high as 10/1, but, one by one, the leading layers slashed the odds before some stopped taking bets altogether.
Of course, it has to be remembered that Henrik Larsson and Owen Coyle had been backed into odds-on to get the job, and both are now sitting at much more generous prices.
Likewise, when the Republic of Ireland were looking for a new manager in 2003, several candidates were placed at odds-on to replace Mick McCarthy.
However, the fact Keane's initial dismissive attitude when first linked with the Celtic position has mellowed appreciably over the last few days is significant.
And, with Martin O'Neill giving him a ringing endorsement, there is no doubt that he is in the frame.
Major shareholder, Dermot Desmond, is a big admirer of his countryman, who signed for Celtic for six months at the end of his playing career.
The indications are that D-day is almost here, and the fans will soon discover who will be asked to take over.
Michael Laudrup remains one of the contenders, after turning down Granada in Spain.
Coyle, Malky Mackay, David Moyes and Steve Clarke also have their admirers.