The 2009 champion retired from F1 after the 2016 campaign and has since focused on endurance racing, winning the 2018 SUPER GT title in the same year he made his only Le Mans appearance to-date for LMP1 privateer SMP Racing.
Due to the pandemic, Button's 2020 racing exploits have been limited to a one-off appearance in the British GT championship at Silverstone, driving a McLaren 720S GT3 for the Jenson Team Rocket RJN squad he co-owns with Bob Neville and Chris Buncombe.
Button, 40, said he is eyeing an opportunity to return to the 24-hour classic "in a competitive car to go for the outright win" but said his "dream" would be to contest the race with his own squad if it could attract support from a manufacturer.
Next year, the FIA World Endurance Championship will replace the moribund LMP1 class with Le Mans Hypercars (LMH) for road-based and prototype machines, while LMP2-based LMDh machines that will also be eligible to compete in the IMSA WeatherTech SportsCar Championship will race at Le Mans from 2022.
"If I could race there next year, and it was the right situation, I would," Button told Motorsport.com.
"The dream obviously would be for this team to race at Le Mans and the dream would be to be in the car when that happens.
"I might be too old by then, I’ll have to wait and see. I feel like I’m 20 years old still, so the reactions are still there, there’s just a few more wrinkles but that doesn’t matter when you’re driving a racing car."
#11 SMP Racing BR Engineering BR1: Mikhail Aleshin, Vitaly Petrov, Jenson Button