Chris Coleman, who led Wales to the semi-finals of EURO 2016 in France, stepped down after failing to lead them to next year's FIFA World Cup finals in Russia and was appointed Championship side Sunderland's manager on Sunday.
Bellamy told Sky Sports: "I'm passionately Welsh. It's the pinnacle for me and I would definitely always be interested in that job.
"It's a good position so I'm sure there are going to be plenty of people interested in it..."
Fellow pundit John Hartson, who has 51 caps for Wales, believes his extensive coverage of the national team merits consideration along with the fact that he was in contention with Gary Speed for the job in 2007.
The 42-year-old says he would "walk on broken glass for the job" but believes he will not be seriously considered by the Welsh FA and tipped recently sacked West Bromwich Albion manager Tony Pulis to succeed Coleman.