According to well-placed sources, senior executives at the corporation have been wooing Radio 2 Breakfast Show host and self-confessed petrol-head Chris Evans, in the hope he will agree to take over.
Evans, 48, who has one of the most prestigious car collections in Britain, including a 12 million ($23.4 million) 1963 Ferrari 250GTO, had previously ruled himself out, but bosses are keen to persuade him to sign up.
It is not clear if Clarkson's co-presenters, James May and Richard Hammond, will remain with the television programme.
It is thought Clarkson may sign for US network Netflix, which is becoming popular with global TV audiences.
Despite feeling he has been left with no alternative but to sack Clarkson, Lord Hall was expected to thank him for helping to build Top Gear into one of the corporation's crown jewels and praise him as a "brilliant broadcaster".
But the decision to continue with the programme will be regarded as something of a risk for the BBC.
For many fans it was Clarkson's near the knuckle brand of humour that helped make the show so popular.