Reports in Scotland on Saturday morning indicated the Bhoys were close to announcing Mowbray as their new manager - subject to the two clubs agreeing a reported £1.5million compensation.
But the Baggies remained adamant they had yet to be contacted by the Bhoys.
A West Brom spokesman said: "I can confirm that we have received no approach from Celtic regarding Tony Mowbray."
Celtic are keen to appoint a quick successor to Gordon Strachan, who resigned a fortnight ago after taking the club to three SPL titles.
They would have to pay Albion compensation should the Midlanders agree to release Mowbray and if the former Celtic player indicated he wanted to leave.
But West Brom have stressed all along they expect Mowbray, who has two years remaining of his contract, to be in charge next season.
The Bhoys were also understood to be interested in Swansea's Roberto Martinez, who has since been approached by Wigan.
Owen Coyle has expressed his desire to stay with newly-promoted Burnley after steering them to promotion to the Premier League.
Motherwell's Mark McGhee, ex-Portsmouth manager Tony Adams and former Celtic players Roy Keane and Henrik Larsson have all been linked with the post.
Mowbray had asked his players to show loyalty at the end of the season and try to help Albion gain promotion back to the Premier League at the first attempt.
It remains to be seen whether the former Hibernian boss shows the same commitment or finds the lure of Celtic too strong to turn down.