The 63-year-old, who has hosted the BBC’s flagship Saturday night football show since 1999, sees his current contract with the broadcaster expire at the end of the season.
Lineker is the BBC’s highest-earning presenter with a deal worth £1.35 million.
According to The Sun, Lineker is now in talks to extend his stint with the BBC and has volunteered to take a £350,000 cut on his current contract.
The report adds that Lineker will hold further talks with BBC executives in October over a new deal that will last at least a further two years.
A source told the newspaper: ‘Gary is hugely popular with both fans and players alike. The sense is that, with so much uncertainty and scandal at the BBC, right now viewers are crying out for a safe pair of hands.
‘Gary adores the BBC, and loves his job, and recognises what an honour it is to host television’s flagship football show, as well as international games.
‘Gary has long maintained that the BBC provides excellent value for money – and has quite literally put his money where his mouth is, and offered to take a substantial pay cut.’
Jermaine Jenas had been one of the frontrunners to succeed Lineker as Match of the Day host before the former Tottenham, Newcastle United and England midfielder was sacked by the BBC last month for sending unsolicited texts to two female staff members.
Jenas, who is a father-of-four, has said he felt ‘ashamed’ of his actions and that he was ‘deeply sorry’ for what happened in the lead-up to his sacking.
BBC Radio 5 Live presenter Mark Chapman, who also fronts Match of the Day 2 on Sunday evening, has also emerged as a strong candidate to replace Lineker.
Chapman also presents the BBC’s new Champions League highlights show, which began this week.
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