LONDON — Is the end of the road in sight for Jeremy Clarkson’s relationship with the BBC? The presenter of hit motoring show “Top Gear” may quit, even if he is cleared of an allegation that he punched one of the show’s producers, leading to his suspension.

The BBC is set to pull the remaining episodes in the present season of the show, which has a global audience estimated at more than 350 million in 214 territories, following the incident. The next two episodes have been removed from the BBC schedules already, and a third, the final of the season, is unlikely to air either.

Clarkson’s relationship with top BBC executives has deteriorated to the point where he may jump even if he isn’t pushed. “Can I see him going back to film another BBC (season)? I don’t think so. But he’ll be fine. The other broadcasters will bite his arm off,” a source close to the presenter told Radio Times magazine Wednesday.

Clarkson’s contract and those of his co-presenters, James May and Richard Hammond, expire at the end of this month and they have not yet signed new three-year deals. The BBC’s free-to-air rivals, ITV and Channel 4, and pay TV operator Sky have all made attempts in the past to persuade Clarkson to jump ship.

Clarkson has taken a relaxed approach to this week’s crisis. He told the Sun newspaper: “I’m having a nice cold pint and waiting for this to blow over.” Outside his London home earlier today, he told reporters that one benefit of the suspension was that he’d be able to watch his soccer team. “At least I’m going to be able to get to the Chelsea match tonight,” he said.

Clarkson was suspended after an allegation that he punched one of the show’s producers, Oisin Tymon, over a dispute about the lack of hot food after a day’s filming. An investigation is taking place into the incident, which is believed to have happened last week.

A petition calling for Clarkson’s reinstatement, set up by political blogger Guido Fawkes, has been signed by more than 470,000 people.

Clarkson and “Top Gear” have often stirred up controversy, which culminated last May in the BBC delivering a “final warning” to the presenter, after allegations he used a racist term while filming the show. The BBC told him that if he made “one more offensive remark, anywhere, at any time” he would be sacked.