He has reportedly met with Australian rugby officials about the prospect of featuring in the 2023 France World Cup.
Vunivalu is contracted at the Storm next season, with the potential offer from Rugby Australia for 2021-23 estimated to be worth nearly $2 million.
It is believed that the Storm could grant the winger an early release to free up salary cap space.
The revelation comes after Vunivalu’s recent Bali controversy where he was king-hit at a night club.
If granted an early release by the Storm, the Fijian can put put pen to paper with RA and can begin negotiations with Australian Super Rugby franchises this year or next.
The Melbourne Rebels could be a potential landing spot as he is based in the city.
Vunivalu has scored 72 tries throughout his 94 NRL appearances and has scored a further 12 tries in Fiji Tests.