The Storm on Thursday granted Asofa-Solomona's request to leave the club, allowing him to "consider other opportunities".
The New Zealand prop has been linked to a move to breakaway rugby competition R360, and would also be expected to command interest from rivals in the NRL.
One of the Storm's longest-serving players, Asofa-Solomona has been a cornerstone of the club's pack since his debut in 2015.
But he has been suspended for the past two grand finals, with Melbourne desperately missing his size and power in losses to Penrith and Brisbane.
In all, Asofa-Solomona played 215 games for the Storm and won premierships in 2017 and 2020. He attended the club's awards night on Wednesday.
The 29-year-old was on a contract of nearly $850,000 a season, meaning his exit will hand Melbourne room to move in their cap.
It will also prompt questions over whether Asofa-Solomona will be one of the first players to sign with R360, given the 201cm front-rower grew up playing rugby.
"I have been committed to the Storm since signing as a junior in 2011," said Asofa-Solomona, who was named in New Zealand's Pacific Cup squad this week.
"With over 10 years now at the top-level and given all I have achieved with the club, I have chosen to step away and consider other opportunities and new challenges.
"I've loved my time in Melbourne.Â
"I'm very thankful to all the players, coaches and staff that I had the privilege to work alongside during my time at such a prestigious club."
Asofa-Solomona is one of two Storm stars linked to the R360 competition, with Ryan Papenhuyzen having also confirmed talks with the rebel league.
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