Melbourne's reported $750,000-a-season extension offer has been rejected by Cameron Munster, who earns $1.1 million annually.
His Storm contract runs through 2027, while the tax-free appeal of expansion side PNG Chiefs is strong.
Munster, 32, has never reached November 1 as a free agent, though he previously rejected a major Dolphins offer before re-signing with Melbourne.
His first finals absence in 2026 ended the Storm's 15-year postseason streak after a disappointing campaign.
Munster hopes to stay in Melbourne: "I'm not saying I'm leaving, I love the club and hopefully we can come to an agreement," he said.
The 256-game playmaker's Rockhampton roots make Queensland appealing, but he has ruled out Sydney as a future home.
He has declared the World Cup his last and wants to repay selectors' faith after his poor NRL season.