Button will join Jimmie Johnson and Mike Rockenfeller behind the wheel of the Hendrick Motorsports-prepared Chevrolet Camaro at the 24 Hours of Le Mans later this year as a Garage 56 entry.
The 43-year-old didn't say no to the prospect of potentially running NASCAR Cup races in the future, though says he would only be interested in road courses - and due to recent schedule changes at NASCAR's highest level, there's no shortage of those.
"Ovals for me is something where I really respect what the guys do, because it's far beyond anything I've experienced," explained Button in a Saturday media availability.
"Always racing with a little bit of yaw all the way through the corner; racing that close to each other and so close to the wall is a skill I don't have — I don't think — I don't know. I've never tried it. But road courses, I'm definitely interested."
He expanded on that more later, saying he wouldn't want to do a one-off like fellow F1 World Champion Kimi Raikkonen did last year.
"I would definitely be interested in racing on street circuits, road courses, but I just don't want to jump in for one race - that's not exciting to me," he said in response to a question from Autosport.
"You can come away from it going 'Oh I did a good job' [but] you're not at your maximum. I would want to do all of the road courses if I'm going to do them.
"We'll see. That's an option. Obviously, the car is a little bit different to what we'll be racing at Le Mans. Less downforce, heavier, less power, and all of that. It's probably tricky, but I would jump at the chance if I had the opportunity."
NASCAR typically only had two non-oval events on the 36-race Cup Series schedule. But that has changed in recent years, with six road/street courses as part of the 2023 calendar.
Johnson, who recently became a co-owner of the Petty GMS (now Legacy Motor Club) Cup team, would be open to extending an invitation for Button to drive for his organisation in the Cup Series.
"I'm sure it's on his [Button's] mind and I know it's on my mind as a car owner now," Johnson told Autosport.
"There's nothing I would like more than to run Jenson at some point.
"I think this is an opportunity for all of us to show our versatility. Rocky [Rockenfeller] has done a great job of capitalising on the opportunity with Action Express and being around the NASCAR community, and he got two drives last year on road courses in NASCAR.
"I imagine it's in the back of Jenson's mind. Of course, a proper opportunity would really sway his mind.
"I think I can talk him into it. We haven't had much conversation about it, but the third car that I'm driving - the #84 car - the commitment we're making to that programme, we need to run the car more.
"So, hopefully we can find funding and interested drivers and figure out how to run that car more often."
Additional reporting by Jamie Klein
