According to the Daily Mail, the TV presenter referred to Brown as a "c***" as he chatted to a live studio audience during a not-for-broadcast warm-up segment.
The alleged incident comes just months after Clarkson came under fire for describing the politician as a "one-eyed Scottish idiot" during a press conference in Australia.
Speaking to fans on Wednesday, it is believed that Clarkson remarked: "I get into trouble talking about Gordon Brown, he is a silly c***."
Though BBC Two controller Janice Hadlow is understood to have spoken to Clarkson following his comments, the corporation has denied reports that he was given a "dressing down" in front of crew members.
A spokesperson insisted: "As controller of BBC Two [Janice Hadlow] holds both the programme and Jeremy in high regard. After the recording she and Jeremy had a discussion about the programme, as controllers and presenters often do."
Clarkson, currently filming for Top Gear in Belfast, is said to be unavailable for comment on the matter.