The BBC is said to be eager to keep Jeremy Clarkson's former Top Gear co-hosts on the show despite his departure.
James May and Richard Hammond have been offered deals in the region of £1m (€1.36m) a year to stay with the hit motoring show, according to The Times.
Such a deal would make the pair among the broadcaster's highest earners.
It comes amid speculation that the BBC will not directly replace Clarkson, but instead have a guest host on each show.
It used a similar tactic when another of its best known faces - Have I Got News For You host Angus Deayton - was fired after reports emerged of drug use and encounters with prostitutes.
A BBC spokeswoman and representatives of the two men declined to comment, but bookmakers have slashed the odds on the pair returning.
"Just a week ago we were offering 5-1 for them to return for another series of Top Gear but following news of the sums that have been offered to the pair we have slashed the odds to 5-4," said William Hill spokesman Rupert Adams.
All three men's contracts ran out earlier this year, and the BBC refused to renew Clarkson's after his much-publicised attack on Top Gear's Irish producer Oisin Tymon.
The show's former executive producer - and old school friend of Clarkson - Andy Wilman has left the show, which sparked rumours that he was joining up with all three men to make an alternative programme, with Netflix and ITV among the broadcasters rumoured to be in the running to show it.
BBC2 controller Kim Shillinglaw, the woman tasked with putting the programme back together after Clarkson's departure, has previously refused to rule out a return to the show for May and Hammond.
Speaking in April, she said conversations were "ongoing" with the pair and confirmed that scenes filmed before Clarkson was suspended were likely to air this summer.
Several names have been put forward as possible replacements for Clarkson, including Guy Martin and Jodie Kidd, but another contender, Dermot O'Leary, has ruled himself out.
The former X Factor host told the Daily Mirror he had not been approached about the job.