Harry Grant, 28, has played 141 NRL matches, 17 State of Origin games and 14 Tests, and is expected to represent Australia at the Rugby League World Cup from October 15.
Melbourne Storm owner Matt Tripp expects the hooker to recommit before November 1, despite a player option in Grant's contract for 2028.
The deal was initially announced as running through 2028, but the option means Grant is technically off contract after 2027.
Without an agreement by November 1, rival clubs, including the PNG Chiefs, can approach him.
The Chiefs, led by coach Wilie Peters and head of football Michael Chammas, are building a squad to compete from their first season and could pursue an elite hooker.
"I don't think he'll go to November 1, but he has got that option," Tripp told News Corp.
Tripp also told News Corp he was trying to persuade Grant to stay.
"I don't think he wants to go anywhere. I think he had in his head a bit like a lot of them - that it'd be interesting to test the market.
"I just said, 'Let me convince you otherwise'.
"So, that's what I was trying to do."
Grant will remain Melbourne captain next season regardless of the contract outcome, though World Cup commitments may limit negotiation time.