The Baggies are adamant that the compensation clause in Mowbray's current contract - which has two years remaining - is legally binding.
The Bhoys are desperate to appoint Mowbray as a replacement for Gordon Strachan as soon as possible.
But Albion are equally determined they will not be railroaded into making any decision regarding the former Hibernian manager.
And their stance remains unaltered in that Celtic will have to meet their £2million compensation figure before they can officially talk to Mowbray, who spent four years as a player at Parkhead.
The figure would also rise if Mowbray decided to take assistant manager Mark Venus and first-team coach Peter Grant with him to Celtic.
West Brom chairman Jeremy Peace has made it clear he wants Mowbray to remain at the helm to try to help the club regain their Premier League status.
Mowbray has earned a reputation of being a man of integrity and asked his players at the end of the season to show loyalty to ensure their stay in the Championship is shortlived.
It would be a major surprise if he took the radical step of resigning should the two clubs not agree a compensation figure despite being told he has to reduce his playing staff for next season.
He also retains the faith of the majority of supporters who wore Mowbray face masks at the final game of the season at Blackburn, even though relegation had already been confirmed.
Albion's viewpoint remains that the ball is firmly in Celtic's court and they must pay the full amount of compensation.