Former BBC Moto GP anchor Suzi Perry, current BBC F1 pitlane reporter Lee McKenzie and BBC Radio 5 Live's Mark Pougatch are said to be in contention to succeed Humphrey, who is taking up a new job fronting BT Vision's Premier League football coverage.
[Left: Suzi Perry / Right: Lee McKenzie]
The Daily Telegraph reports that BBC bosses are favouring a female anchor to work alongside existing pundits David Coulthard and Eddie Jordan.
Perry is believed to be the frontrunner, although McKenzie is held in high esteem within the F1 paddock and previously anchored the show when Humphrey was working at the 2010 Commonwealth Games and the London 2012 Olympics.
Chris Evans, who had previously been linked with the role, is no longer thought to be in contention due the potential for conflict with his existing commitments at BBC Radio 2 and The One Show.
He is also said to have been reluctant to travel to races which the BBC did not have live as part of its F1 rights-sharing deal with Sky.
The final decision could be made as early as next week.