Stopped by a BBC News crew outside his home, May was asked if he believed that Clarkson was innocent of punching a producer.
May responded, "I think he's been involved in a bit of a dust up, and I don't think it's that serious".
Closing out the conversation, May indicated that the incident took place over dinner and that he was not present when the "dust up" occurred.
Later in the day, in footage filmed by ITV News and 5 News, May was asked if he supported Clarkson, to which he responded: "In many ways no. I've said many times before the man is a knob, but I quite like him."
He also indicated that the situation was "all getting a bit ridiculous" and that he had no further light to shed on the event as he was "blind drunk" at the time.
Clarkson made news yesterday when he was officially suspended by the BBC over a "fracas", which is currently the subject of an internal investigation. The corporation also decided to remove Top Gear from its programming schedule, with a documentary about the Red Arrows aerobatic display team replacing the motoring show on BBC2 this Sunday.
According to a report in Radio Times, Clarkson threw a punch at one of the show's producers last week, but the incident wasn't reported to BBC management until early this week.
Last year, BBC director general Tony Hall placed the outspoken Top Gear on his "final warning" after footage, which was not aired on the show, leaked out showing Clarkson mumbling his way through a version of "Eeny, meeny, miny, moe" that included the n-word.