The two leading contenders for the managerial vacancy at Celtic appear to be ruled out of the running.
But Coyle has pledged his future to the Clarets, while the Baggies issued a hands off warning to Celtic over Mowbray.
Coyle, who has just led Burnley into the top flight of English football for the first time in 33 years, was believed to be the Hoops' number one target.
However, Turf Moor chairman Barry Kilby revealed this afternoon the 42-year-old was "very close" to agreeing a two-year extension to his current contract and blasted the speculation that has surrounded his manager.
Reports claim Coyle held talks with Celtic chief executive Peter Lawwell earlier this week and it was telling that he would only deny any "official" approach had been made for his services when questioned about the link this morning.
Coyle told Sky Sports News: "I'm very much focused on what we are going to hope to do in the Premier League.
"It is an exciting challenge and one I am looking forward to.
"I think the fans know the rapport I have with this football club.
"We think we have an exciting prospect and challenge ahead of us and we want that to continue.
"I'm as focused today as I was the first day I came into this job. I wanted to build this club and take it forward.
"What an exciting prospect to pit your wits against the best managers in world football with the best players and best teams - it's the best league in the world."
Coyle was a boyhood Celtic supporter and the Scottish-born former Republic of Ireland international acknowledged the fears of Burley fans that he might leave because of his past affinity for the Glasgow club.
He said: "Obviously, they can see the attraction Celtic would hold to someone like myself, growing up as a Celtic supporter - but it's all hypothetical.
"I'm flattered because it's Celtic you are talking about, given the size of the club, but that's all it was, speculation.
"There was never any approach so I am not going to get into the realms of talking about stuff that doesn't exist.
"There was no approach, so there wasn't anything to talk about and equally I am still committed to Burnley Football Club."
Coyle's declaration has shifted the focus to Mowbray, whose West Brom side have just been relegated from the Premier League.
The former Celtic defender - who invented the famous huddle at Parkhead - has yet to comment on being linked to the job.
But his current club are adamant the 45-year-old is going nowhere.
"We have already made our position very clear on this situation and it has not changed," the Baggies said in a statement.
"We have not received an approach from Celtic for Tony Mowbray - nor would we welcome one.
"Tony is under contract for the next two years and we fully expect him to remain as our manager."
Swansea have also confirmed there has been no approach from Celtic for their manager, Roberto Martinez.
Wednesday saw Dundee United boss Craig Levein dismiss speculation linking him with Parkhead, while the agent of Slaven Bilic claimed the Croatia boss would be interested in succeeding Strachan.