Speaking after the meeting, May said they had just been "having a pint," adding that he still didn't know what he would do in the future.
Hours later, a BBC spokeswoman confirmed that Mr Wilman, who attended the £10,500-a-term Repton School in Derby with Clarkson, had handed bosses his resignation.
Earlier, May ruled out returning to Top Gear without Clarkson, insisting it would be "lame" with a new presenter in place of his sacked co-host.
The 52-year-old said the BBC would be "stupid" to try a version of the programme with "a surrogate Jeremy," Hammond and himself - adding that the idea was a "non-starter".
His comments mean that if the show does return next year, it will likely be with an entirely new presenting team. Both May and Hammond saw their contracts finish last month.
May told The Guardian: "Me and Hammond with a surrogate Jeremy is a non-starter, it just wouldn't work. That would be lame, or 'awks' as young people say.
"It has to be the three of us. You can't just put a surrogate Jeremy in and expect it to carry on. It would be forced. I don't believe they would be stupid enough to try that.
"It doesn't mean I won't go back - we may all go back in the future. It might just be we have a break from it. I don't know. It would be a bloody tough call to do Top Gear without Jeremy."
It comes a day after BBC2 boss Kim Shillinglaw, who has been tasked with finding a replacement for Clarkson on Top Gear, said the 55-year-old presenter "will be back on the BBC" at some point.
Shillinglaw also confirmed Clarkson's final Top Gear scenes will be screened later this year and she was not thinking of his replacement "in terms of gender".
Clarkson was sacked by the BBC after an "unprovoked physical and verbal" attack in North Yorkshire that left his victim, Top Gear producer Oisin Tymon, in need of hospital treatment.
The star was suspended last month when he became the subject of an internal BBC investigation after he attacked Tymon, 36, splitting his lip and verbally abusing him.
Clarkson's contract was not renewed, with director-general Tony Hall saying at the time 'a line has been crossed' and 'there cannot be one rule for one and one rule for another'.
Clarkson said he considered turning his back on presenting altogether in the immediate fall-out from the incident, but has since stated that he expects to present another TV show on cars in the future.
Earlier this month, North Yorkshire Police said that following an investigation Clarkson would face no further police action over his attack on the producer at a hotel in Hawes.
Meanwhile, Clarkson revealed in a newspaper column earlier this month that he was told by a doctor that he might have cancer, two days before assaulting Tymon.
Top Gear is viewed by more than six million viewers on BBC2 and watched in more than 200 countries.
- Daily Mail
