He also drove a Triple Eight-prepared Sandman Supercar at Sandown in 2016.
Having aligned with Brown at McLaren, Ricciardo said he is keen for both a Bathurst Supercar run and IndyCar start.
"I do have to ask Zak. I need to – even if I don’t do the race – I need to drive a Supercar around Bathurst,” the 31-year-old said in this month’s edition of GP Racing magazine.
"Whether it’s a private test, or the actual race, I do need to do it. And I think now I have a good opportunity with Zak as a friend and a boss.
Ricciardo drove Triple Eight's Sandman in 2016
"He’s keen to try and get us into the other open-wheelers in the States, the IndyCars. So there’s a lot to do.”
In 2019, the Perth-born racer said he would “love” to steer a Supercar around Mount Panorama.
Calendar clashes would likely be the barrier; this year’s Repco Bathurst 1000 falls on the same weekend as F1’s Japanese Grand Prix.
The Bathurst 12 Hour, which will return in February 2022, could be another option.
"When I signed with [Brown], over the early phase of last year, we had these conversations and it was thrown in there: 'We should get you to do the 12 Hours of Bathurst’,” Ricciardo said.
WATCH: RICCIARDO ON KELLY SUPERCAR DRIVE
"If he asked me and it worked logistically, I would say yes.”
Ricciardo will continue his 2021 F1 campaign at Imola this weekend, having scored a seventh-placed finish at the season-opening Bahrain Grand Prix.
The Repco Supercars Championship field will return to Symmons Plains for the Beaurepaires Tasmania SuperSprint across April 17-18. Tickets are on sale now.
The event will be broadcast live on Foxtel and will be streamed on Kayo.