Though he said that Prime Video had not cancelled the motoring show, he did say it was coming to a "natural end".
Speaking to the Radio Times, May said: "I mean, some people have said we've been cancelled. But really we're getting quite close to the end of our contract, but we didn't really have any particular plans to keep going because we're all really just getting a bit old.
"It might be time to let someone else have a crack at it."
He added that the trio of himself, Clarkson and Richard Hammond would still continue to make TV: "It doesn't mean we're going to stop making TV.
"We might still make our individual things: farming or science or mending cars or whatever it is we get up to. But I don't know, to be honest. No one has told us to go away. It's reaching its natural end, like parties do. There comes a point at 4am when it is over."
Watch the trailer for The Grand Tour: Eurocrash
There were reports earlier this year that Amazon had cut ties with Clarkson following the fallout over his newspaper column where he said he "hated" Meghan Markle and dreamt about her being pelted with excrement.
Clarkson later apologised for his column and admitted that Amazon were "incandescent" about his words regarding the royal.
In a since deleted apology on Instagram, Clarkson wrote: “I really am sorry. All the way from the balls of my feet to the follicles on my head. This is me putting my hands up. It’s a mea culpa with bells on.”
Meghan Markle did not accept Clarkson's apology.
The Grand Tour returns to Prime Video on 16 June.
Watch below: James May 'hospitalised after crashing into a wall at 75mph'