The Queensland winger's transition from league to union over the past two years has been far from smooth, with a string of injuries stalling his progress.
He broke into the Wallabies set-up for the England series last year but has not been seen in a gold jersey since running off the bench in the 76th minute of the decider at the Sydney Cricket Ground against Jones's England.
Jones, now coaching Australia for a second time, has long had a soft spot for rugby league converts and told the Australian Associated Press last week that Vunivalu could break into his squad.
Vunivalu said he was encouraged by Jones's endorsement ahead of his first Super Rugby Pacific clash against Western Force in Melbourne on Sunday.
"It gives you a boost of like, you know, trying to get better, play better to get picked," Vunivalu, who missed the Reds' season-opening 47-13 loss to the Wellington Hurricanes with an ankle injury, told reporters.
"I feel good. Heading out this week I just want to focus on my footy. Stay injury-free and play out the whole of Super Rugby Pacific."
Australia has no shortage of quality wingers, with Marika Koroibete a bolted-on starter and Mark Nawaqanitawase emerging last year to challenge the likes of Andrew Kellaway and Tom Wright.
Fans had hoped Vunivalu might have staked a bigger claim by now, having starred in Australia's National Rugby League competition with the Melbourne Storm.
Vunivalu said he felt under pressure to work on his speed under Rennie, leading to injuries and confidence problems.
"I've never been that guy, I never hit top speed until game day ... I'd been focused too much on trying to get my speed back, I forgot about the footy," he told AAP.
"Now that's behind me ... I just want the footy in my hands again."
