Jonathan Ross is said to have offered to accept a 50 per cent pay cut - which would slash his annual salary by £3m.
The 49-year-old radio and TV presenter is also thought to have agreed to shorten his contract to two years.
His current three-year deal, put at £6m a year, is due to run out in 2010 and he could be paid £3m a year under a new offer.
It is understood discussions over the final deal and settlement figure are still being hammered out.
Last year, the chat show host was suspended for three months after he and Russell Brand left lewd phone messages for Fawlty Towers actor Andrew Sachs.
Around 40,000 complaints were made about the prank calls, which were broadcast on Brand's Radio 2 show.
The BBC has also come under pressure over the past year to reveal details of the pay of individual stars.
A source close to the star told The Sun: "Jonathan is happy to stay at the BBC and is fully aware he needs to take a pay cut.
"He has offered to take a 50 per cent pay cut and will be committed to his TV and radio shows."
The BBC said it did not discuss artists' contracts.
© Press Association