Matt LeBlanc has threatened to quit as Top Gear host if Chris Evans is not sacked.
Reports suggest that the former Friends actor is becoming increasingly frustrated with how rude his co-presenter is with the staff on set and has told producers that they can no longer work together.
The revelations are said to have rocked the BBC and could leave them having to pick between the pair, with filming for the second series due to start in September.
A show source said: "The big question now is who goes and who stays."
A BBC spokesman and a spokesman for Evans, 50, declined to comment on the reports.
But a spokeswoman for LeBlanc told the Sunday Express: "Nothing has been discussed or decided."
The fourth episode of the revamped BBC Two motoring show was broadcast last Sunday, with overnight ratings slumping to a new record low of just 2.3 million.
This was down from the previous week's total of 2.4 million, which matched the lowest in the programme's history, and a further fall from 2.8 million for episode two and 4.1 million for episode one.
Evans, who also presents BBC Radio 2's breakfast show, has defended the performance of the relaunched motoring programme in recent weeks, calling the new Top Gear "a hit".
However, audience appreciation figures showed Evans's debut episode was rated by viewers as the worst-quality show on terrestrial TV on the weekend that it aired.
Evans has been under intense scrutiny since he agreed to take over the show, and has been panned by viewers for being "too shouty" and behaving like "an embarrassing dad".
He was named as the new host last year, following the departure of controversial frontman Jeremy Clarkson after what was described as a "fracas" with producer Oisin Tymon.
It was revealed that the row, which happened in a North Yorkshire hotel, took place because no hot food was provided following a day's filming.
His dismissal prompted a mass walkout as Richard Hammond, James May and Andy Wilman, the executive producer - and an old school friend of Clarkson's - all resigned.