Mowbray's stock remains high with West Brom's chairman and fans
Celtic would have to pay about £1m in compensation to prise Tony Mowbray from West Brom, BBC Sport understands.
The 45-year-old has been installed as favourite by some bookmakers to replace Gordon Strachan, who left on Monday after four years in charge of the club.
But it appears that West Brom's demand could put him out of Celtic's reach.
And, although Mowbray is believed to be interested in talking to his former club, he would not speak to them until a financial package had been agreed.
The ex-Celtic defender is regarded as a man of principle and, as he has two years left on his contract, would not walk away without some form of compensation deal being reached.
Celtic are searching for a new manager after Strachan quit following his side's failure to win a fourth Scottish Premier League title on Sunday.
Tony Mowbray is under contract for the next two years and we fully expect him to be our manager next season
West Brom statement
Former Celtic defender David Moyes is many fans' choice to take over at Parkhead but is highly unlikely to be tempted away from Goodison Park.
And any hopes the Glasgow club might have had of appointing self-confessed Celtic fan Owen Coyle as their successor are likely to have been diminished by Burnley's promotion play-off victory on Monday.
While Coyle expressed his desire to test himself in England's top flight, where his club will take the place of the Baggies, Mowbray could have become a more realistic target after his club's relegation.
The Midlands club were dismissive of the suggestion that Mowbray could be a target for Celtic.
"Tony Mowbray is under contract for the next two years and we fully expect him to be our manager next season," West Brom said in a statement.
"Further than that, the club feels there is no need to comment on speculation."
West Brom told the former central defender - who spent four seasons with Celtic, sandwich between spells with Middlesbrough and Ipswich - last week that he must trim the size of his senior squad for next season from 31 to 20 players.
And he had been informed before the end of the campaign by Baggies chairman Jeremy Peace that there will be no new funds available for transfer dealings as he looks to reshape his squad.
However, Mowbray has publicly insisted he is happy with the parameters he has to work within West Brom.
Mowbray led the Baggies to promotion from the Championship 12 months ago during his first full season in charge.
Promoted Burnley say they will not be waving goodbye to Coyle
They were, however, then instantly relegated from England's Premier League for the third time in seven years on 17 May.
Yet Mowbray has retained the support of the majority of the Baggies supporters as he refused to compromise his beliefs and continued to play a passing game despite poor results.
It is the kind of football that is also likely to please Celtic fans, who were critical of the style of play under Strachan, despite his team's success on the field, and will appease those who felt the former manager needed to be more "Celtic-minded".
Strachan, for his part, has recommended his former Aberdeen team-mate Mark McGhee, the former Celtic striker now managing Motherwell, for the job.
Other names being linked with the post are Dundee United's Craig Levein, Ipswich's Roy Keane, Croatia's Slavan Bilic, former Celtic midfielder John Collins, who has quit as Charleroi coach, and Lech Poznan's Franciscek Smuda, whose claim that he had already been lined up as Strachan's successor was recently rubbished by the Parkhead club.
Celtic chief executive Peter Lawwell was in London on Tuesday as his search for a new manager continued, but no appointment is imminent.
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