Munster's management confirmed on Saturday the Storm superstar had knocked back Melbourne's two-year, and would hit the market on November 1.
The 31-year-old is signed until the end of 2027 and has been at Melbourne since his 2014 debut, but has regularly flirted with the idea of leaving the club.
He went incredibly close to signing with the Dolphins for 2024, and has already been granted permission to negotiate with the PNG Chiefs before November.
Speaking after Saturday night's last-minute win over Cronulla, Bellamy suggested he wanted Munster to finish his career at the Storm.
"We'll do everything we can to keep him," Bellamy said.
"But if he sees that it's better for him, his family or whatever situation to move on, he'll go with our blessing, without a doubt.
"He's a wonderful player, a wonderful clubman. And if he sees himself off going to another club, we're not going to argue with that.
"He's been there a long time. He'd come to our club as a 17-year-old and he's always done the right thing by the club.
"But as I said, we'll try and do everything we can to keep him, without a doubt."
The five-eighth's future could well be tied to Bellamy's given the pair's close bond and the fact the veteran Melbourne coach is expected to make 2027 his last in the role.
Assuming he sees out the rest of this contract and plays for Melbourne next year, Munster will overtake Ryan Hoffman into the top-five most-capped players at the Storm.
Munster did not speak to reporters as he left Shark Park on Saturday night, but briefly addressed the issue on a TV cross after the Storm's win.
Asked by Cooper Cronk about the situation, Munster made a wisecrack back in a likely reference to the former halfback's decision to leave for Sydney Roosters after 2017.
"Don't be throwing stones in glass houses, Coops," Munster replied when Cronk told him of his shock about the news.
"It's a media beat up.
"With my new manager now Justin (Caines), I got rid of Braith (Anasta after he stopped being a manager). He has been doing some good stuff for me now."
Munster then quipped he was "going to the world ... overseas to St Helens", in a reference to new Saints coach Kevin Walters sitting alongside Cronk on the Fox panel.
Munster would be add to a star-studded list of players so far set to hit the market for 2027, headlined by Nathan Cleary and Sam Walker.
He is not expected to end up at the Chiefs, with the 19th franchise prioritising the pursuit of an out-and-out halfback to play alongside Jarome Luai.
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