The statement was almost identical to another two released by the Midlands club in the nine days since Gordon Strachan quit as Celtic manager.
The news comes hours after the Parkhead side appeared to be priced out of a move for Roberto Martinez, with Swansea demanding £2million in compensation for the Spaniard.
Compensation is also thought to be a problem in any attempt to lure Mowbray from The Hawthorns.
It was suggested last week it could take as much as £1.6million to buy out his contract, though more recent reports claim it may only need around half that amount.
Mowbray has been one of the favourites for the Celtic job since it became available and the lack of any comment from the 45-year-old has only served to fuel speculation he is interested in the role.
Mowbray spent four years at Parkhead in the early 1990s and invented the famous 'Celtic Huddle'.
He would tick many of the boxes of both the club's board and fans, having prior links to the Hoops as well as being renowned for an attacking brand of football.
However, there are question marks over his adaptability after West Brom won the Championship last year only to finish rock-bottom of the Premier League this term.
But he would certainly appear less of a gamble than Martinez, who is one of the youngest managers in British football and who has no top-flight managerial experience.
Yet, former Celtic defender Steven Pressley believes age should not be an issue for the Hoops board.
"I think that if you're the right man, you have confidence in your ability and you treat players in the correct manner then you're ready for the job, regardless of age," said the 35-year-old, who revealed he would relish a return to Parkhead in a coaching capacity after announcing his retirement today.
Other names in the frame to succeed Strachan are Motherwell manager Mark McGhee - who said yesterday he had yet to be approached - and Dundee United boss Craig Levein.
Owen Coyle was thought to be Celtic's first choice but he pledged his commitment to Burnley before going on holiday at the weekend, although he is yet to sign a contract extension.
Meanwhile, PSV Eindhoven general manager Jan Rekers claims the Dutch club are not set to offer Jan Vennegoor of Hesselink a move out of Parkhead.
It had been reported the striker was undergoing a medical with his former side, but that has been dismissed.
"I can confirm we have not spoken to Jan, his agent or his club," said Rekers.