Munster is out of contract after 2027 and, in recent days, the Storm have granted the veteran five-eighth early permission to negotiate with the Chiefs.
Melbourne's most-capped active player, Munster may yet ink a contract extension to remain with the Storm for 2028 and beyond
But the 31-year-old can now entertain advances from the NRL's forthcoming 19th team, who are already assembling an impressive roster that features Jarome Luai, Alex Johnston and Connor Watson.
Munster commands a seven-figure salary at the Storm but the chance for tax-free windfall at the Chiefs could be life-changing for the Queensland captain as he draws nearer to retirement.
Having won two premierships across 251 appearances for the Storm, Munster would have enough credits in the bank to leave on good terms.
"'Mun' has done a whole heap for our club and he's done it over a long period of time," said Bellamy, who handed Munster his NRL debut in 2014.
"He's been a wonderful player with our club, so if he sees that he wants to go to the team in Papua New Guinea ... I'd be happy to let him go."
A decision on Munster's future will come down to discussions between agent Braith Anasta, Storm football manager Frank Ponissi and chief executive Justin Rodski.
"I don't know whether they'll be (making) the same decision as me but he's done a lot for our club, 'Mun'," Bellamy said.
"He's been a valuable servant and very loyal. So if he wants to do that and that's going to help him in later life, well, I'm willing to say, 'Yeah, okay'.
"We'll just see what happens but I'll go on the record as saying if he wants to go and his family wants to go, well, he goes with my blessing."
Storm captain Harry Grant felt it made sense for Munster to begin contemplating his future during his current lay-off with a knee injury.
Players coming into the final year of their contract can typically begin negotiating with rival clubs from November 1.
But Munster is likely to be playing for Australia at the World Cup between October and November this year.
"It'll probably be a bit of a busy time towards the end of the year with the World Cup and everything like that, so I think it's not a bad time for him to have that look," Grant said.
"The NRL have brought a couple of new teams in so I don't think you can hold (grudges against) players for having that opportunity to talk to them."
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