Bellamy has enjoyed his time in charge of Wales, taking his first senior managerial job when he signed a four-year contract in July 2024.
He earned praise for a nine-game unbeaten start, guiding Wales to the top tier of the Nations League and instilling a bold and attacking new style of play.
But their 2026 World Cup qualifying campaign ended in failure, with two defeats against Belgium costing Wales automatic qualification, before they lost at home to Bosnia-Herzegovina in their play-off semi-final in March.
While Bellamy relishes his job, the former Liverpool and Manchester City forward has made no secret of the fact that he wants to manage at the highest level of club football.
The FAW is aware of interest in him from clubs other than Burnley but has some security in the form of a release clause which would require any potential suitor to pay at least £700,000 to buy Bellamy out of his contract.
Bellamy’s former Liverpool team-mate Steven Gerrard has also been linked heavily with the Burnley post, while Cardiff City head coach Brian Barry-Murphy is another potential contender.