The Baggies on Monday confirmed they received an official approach for Mowbray from Scottish giants Celtic, who are searching for a successor to Gordon Strachan following his Parkhead departure.
But Albion said the appraoch was 'not welcome' and pointed out there is a £2million compensation clause in Mowbray's current deal.
Mowbray jumped to the top of Celtic's wanted list after Owen Coyle decided to stay at Burnley after steering them into the Premier League, and he has been backed to be a Parkhead hit by a host of former Hoops stars including ex-Albion frontman John Hartson.
Baggies chairman Jeremy Peace will be loathe to lose Mowbray after three successful seasons under his stewardship at The Hawthorns.
But if the former Middlesbrough centre-back does head north of the border, Peace is being tipped to make a move for Ferguson following his success in steering Peterborough to back-to-back promotions.