The former Melbourne Storm star, who has made one brief Wallabies appearance in a stuttering transition to the new code, has signed a contract extension with Rugby Australia and the Queensland Reds.
Battling injuries early in his rugby career, Vunivalu has slowly started to find his feet this season but faces fierce competition for a Wallabies berth in this year's Rugby World Cup.
Vunivalu made a three-minute appearance for Australia in last year's Test against Jones's England.
But the 27-year-old has a fan in Jones, who selected him in his first training camp squad in April.
"Suli has the potential to be a Test match-winner," Jones said in a statement.
"I'm really pleased how he's been progressing through Super Rugby and even happier that he's committed his future to Queensland and the Wallabies."
The Fijian-born winger scored 15 tries in his first 26 games for the Reds, debuting in the 15-player game in 2021 after a stellar NRL career that included two premierships.
He said he was enjoying playing rugby with the Reds.
"I've learned plenty with the Reds and Wallabies and know there's a long way to go if I want to achieve my goals," Vunivalu said.
"We've got a great group of players and staff at Ballymore. I'm enjoying working alongside them every day.
"It's an exciting year for the Wallabies with the World Cup. I'm doing everything I can to be a part of it after the Super Rugby season."
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