Two-time F1 world champion Alonso competed in endurance racing during his sabbatical from F1, winning Le Mans twice in 2018 and 2019 with Toyota's LMP1 team as well as taking a World Endurance Championship crown.
He hasn't ruled out going back to the French endurance classic in the future even while he is still active in F1.
After this year's running, he said: "I may go. I did the endurance world championship and Formula 1 world championship. I think both championships, so why not one race only?"
According to Verstappen, Alonso has been tapping him up to embark on the project together, claiming that Alonso only wants to return if it's with the Dutchman.
Speaking at the annual Honda Thanks Day at Motegi, Verstappen said: “Le Mans I definitely would like to do.
“I’ve been there already, when my Dad used to race in Le Mans. The atmosphere is amazing, so many people. Driving through the night, sunrise, I think it’s really cool.
"I've been speaking to Fernando about it. He said he would only want to do it with me again. So, I was like 'wow, that would be really cool!'
It is not the first time the topic of Verstappen teaming up with Alonso at the French enduro has come up. Speaking to Motorsport.com late last year, Verstappen said: "I think Fernando will never stop racing. He is probably a little different to me in that sense with the age, but who knows. We need to have a good opportunity. If Fernando goes, he wants to challenge for the win in a competitive car. And I am exactly the same.
"That is also why I don't want to rush the whole project, just because there are so many changes happening at the moment in endurance. I think it is better to wait and see what is exactly happening now and to see how it's going to progress, and then make your mind up. I am not in a hurry."
But unlike Alonso, Verstappen said he doesn't like the idea of competing in Le Mans during his active F1 career, which will run until at least 2028 when his current Red Bull deal expires.
"Not really. I don't think I want to do that, because you want to focus on one thing fully," he explained. "And when you start combining stuff and you can only do one race, you're not really well prepared."
When asked if that meant time would run out for a bid alongside Alonso, he fired back: "I mean, if Fernando keeps racing, I'm sure he'll be as competitive at 50 as he is now!"