Harry Grant may also test the player market, despite Melbourne working hard to secure a deal before November 1, journalist Brent Read said.
Read told Triple M that Munster's management is baffled by the Storm's reported two-year extension offer, worth about $750,000.
The proposed deal would represent a substantial reduction from Munster's current contract, with the shortfall reportedly around $350,000.
"There's a view in the Munster camp that he is the current Queensland captain, he's the Australian five-eighth yet he is being asked to take a $350,000 hair cut," Read said.
"That's why Cameron Munster hasn't taken that deal and I can understand that view point.
"He wasn't at his best this season, but he still captained Queensland... it's a fair hair cut."
Munster is set to become available to other clubs on November 1.
"If anyone is going to go, it's probably going to be Cam Munster... Munster is going to November 1 and Harry looks like he will," Read said.
Read added that Grant's involvement in the Australian team camp could make negotiations difficult, despite Melbourne's efforts to finalise an agreement before November 1.