Richard Hammond and James May have been offered a combined pay offer of £9.2 million to present two more series of Top Gear.
Reports suggest that May and Hammond were earning around £500,000 per series during the Clarkson era, but this latest deal could see them pocket £4.6m, which would make them two of the BBC's highest paid stars.
The two presenters were thought to have quit the show after Jeremy Clarkson was fired for punching Top Gear producer Oisin Tymon in March 2015.
The BBC is desperate to keep the motoring show, because it is the broadcaster's biggest money-earner, according to the Daily Mail.
It is thought BBC chiefs are keen on modelling the show on satirical news quiz Have I Got News For You?, which has a different presenter at the helm for each episode.
A third presenter would replace Clarkson, while Hammond and May – who have courted interest from ITV and Netflix, according to reports – would co-host the show.
News of the possible return of Hammond and May comes as discussions are under way about the future of BBC funding.
The Conservative government is looking into scrapping the £145.50 annual BBC license fee and replace it with another funding system.
Meanwhile, the corporation is planning to save more than £1.5bn every year by 2016/17 after implementing a series of cuts since 2007.
Julian Knight, the Conservative MP for Solihull, criticised the BBC about the reported big-money deal, according to the Telegraph.
He said to the publication: "This is deeply disturbing and shows flagrant disregard for licence-fee payers and many BBC staffers who have to make do on a lot less."
As the debate over the future of the show continues, the three presenters have been featured on the Top Gear world tour, which has been stripped of BBC branding and re-named Clarkson, Hammond & May Live.
The tour will run for six months and take them from Belfast to Sydney to Warsaw before finishing in London this November.