The veteran rockers - comprising Sir Mick Jagger and Keith Richards, both 66, Charlie Watts, 69, and Ronnie Wood, 63, - will reportedly undertake a series of concerts at venues around the world next year and then plan to call time on their epic career.
A source told The Sun newspaper: "They're likely to perform in stadiums. It's almost certainly the last full-scale world tour.
"The band realise that age is creeping up on them. They want to bow out on top of their game, and not short-change their fans."
If the jaunt - which is expected to run throughout next year and well into 2012 - goes ahead, it won't be the 'Satisfaction' group's first farewell tour of their home country.
They famously performed around Britain in 1971 before leaving the country to avoid high taxes.
They gave up touring again from 1982 before returning to the road in 1990.
The 'Brown Sugar' hitmakers - who have sold over 200 million albums since forming in 1962 - last performed together on their 'Bigger Bang' world tour which ran from August 2005 to August 2007. It was the highest-grossing concert series of all time, generating over $558 million.