The highly-rated Cherries chief has been backed into 8-15 with bookmaker Victor Chandler and 1-2 with Skybet to succeed Brian Laws, who was sacked by the Championship club yesterday.
But it was business as usual for Howe, who has also been linked with the top job at Sheffield United, this morning. He was at training and busy preparing Cherries for the League One clash at Swindon Town on Saturday.
Asked if the speculation was a distraction or flattering, Howe told the Echo: It's neither really. I take it with a pinch of salt until told differently.
Howe is six months into a three-year contract with Cherries and chairman Eddie Mitchell last night told the Echo the club had received no approaches for their manager.
Burnley today issued a statement saying caretaker boss Stuart Gray will be in charge for Clarets' next three matches.
¢Don't miss today's Daily Echo for a 16-page supplement marking the 100th anniversary of Dean Court. Features include interviews with John Bond, Steve Fletcher and Darren Anderton.