His current deal is due to expire in 2025, while he's been presenter of Match of the Day ever since 1999.
And it's also claimed that, with the BBC set to secure Champions League highlights, presenting that show 'may appeal' to Lineker.
The former England, Tottenham and Leicester star previously worked for TNT Sports on Champions League nights, when they were known as BT Sport.
The BBC won the rights to show Champions League highlights in June last year.
A report read: "The men's Champions League is to be broadcast on BBC TV for the first time from the 2024-25 season.
"Highlights will be shown from 22:00 on the Wednesday of match weeks on BBC TV, BBC iPlayer and the BBC Sport website and app, with clips for online and social media also available.
"The three-year deal includes the final, with highlights rights to be confirmed.
"It complements the existing BBC Radio 5 live commentary rights for European football's premier club competition.:"
BBC Director of Sport Barbara Slater, who confirmed her retirement in September, added: "We are simply thrilled to have won these rights.
"Our reach and ability to bring people together is unrivalled and we couldn't be more delighted that Uefa has recognised the value in our ability to bring the Uefa Champions League to the widest possible audience across the UK.
"This package of highlights and digital content will allow football fans to follow the Uefa Champions League, wherever and however they like.
"The Uefa Champions League is a wonderful addition to our portfolio of football output on the BBC and we can't wait to get started in 2024."
In July, it was confirmed Lineker was the BBC's biggest earner.
Zoe Ball is second on the list, with the 52-year-old pocketing £984,999 each year.
Alan Shearer and Huw Edwards made the list of highest paid presenters, taking home £449,999 and £439,999 respectively.
Stephen Nolan was next up on £404,999, with Fiona Bruce in sixth on a salary of £399,999.