Richard Childress Racing officials confirmed to Autosport that the team is in discussions with Brown to drive the #33 Chevrolet in the 9 June race at the Sonoma road course.
While the deal is not yet completed, an RCR spokesperson said it was “close” to being finalised with an accompanying official announcement.
Brown, 25, would join Shane van Gisbergen, Brodie Kostecki and Cam Waters as Supercars standouts who have made NASCAR national series starts in the past two seasons.
Brown leads the Supercars standings so far this season with three victories for the Triple Eight Race Engineering Red Bull team he joined over the winter from Erebus as van Gisbergen's replacement.
“I don’t know a lot of detail about it, but I know it’s a good possibility that it’s happening,” said RCR Cup driver Austin Dillon, whose grandfather, Richard Childress, owns the team. “I don’t know that it’s completed yet.”
Brown and RCR have some previous experience racing together. He joined Dillon and Kyle Busch as a last-minute fill-in for Kostecki in a World Racing League event at Circuit of the Americas in December.
“Me, him and Kyle were kind of team-mates on that deal. It was fun,” Dillon said. “It was a last-minute thing. He came in and kind of jumped in there for us.”
“Obviously, those guys are really solid with their car. They have a subtle difference in their driving style, and they use the clutch a little bit more. It’s what they do to keep the tyres on those cars.
“Anytime you can kind of learn for those guys and make the programme better, I think it’s good.”
Last July, van Gisbergen became the first driver in more than 60 years to win a Cup race on his debut when he took victory in the inaugural Chicago Street Race driving for Trackhouse Racing.
The victory served as the instigator for the Kiwi to move to NASCAR competition this season, where he is running full-time in the Xfinity Series while also running part-time in Cup races.
Kostecki, 26, made 16 starts in what is now the ARCA East series in 2013 and 2014 and made his Cup debut last year at the Indianapolis Motor Speedway Road Course.
Waters, 29, has made a pair of starts in the Truck Series this year with ThorSport Racing, most recently in Saturday night’s race at Kansas Speedway.