The move, with senior managers reportedly also considering dropping coverage of the famous Wimbledon tennis tournament, is amid the BBC coming under pressure to cut 20 per cent from its budget by 2014.
The Guardian said the BBC, having taken over Britain's F1 coverage from commercial broadcaster ITV in 2009, currently spends 40 million pounds ($64 million) on the sport per year.
The current contract runs until 2014.
A report in the Daily Mail said F1 is a "non-peaktime product" for the BBC, with its cost "seen in some quarters as an extravagance at a time when cuts are desperately needed".
A BBC spokesman said: "We are looking at a range of ideas and it would be wrong to comment on what is speculation."