The ageing rockers, led by Mick Jagger, are making plans for a world tour that will reach Australia by 2012.
Other big names tipped to be here this year or next include U2, Bon Jovi, the Eagles, Peter Gabriel, America, Leona Lewis, Chicago, Roxy Music, Billy Joel and Elton John.
"The Stones are coming - and they want crazy money," a respected tour promoter told theSunday Herald Sun.
The Stones will play stadiums and have already rebuffed other overseas offers of $2.4 million a show.
A local promoter who pitched $14.4 million for six shows in three cities was told by agents for the Stones: "You are not even in the ball park."
People in the Stones camp say US drummer Steve Jordan will stand in for Charlie Watts, who has vowed to quit world touring.
And they say guitarist Keith Richards has reconvened the band to make a new album and take a show on the road.
"This has been rumbling for the last 18 months. Offers are on the table," a source said. "An announcement and dates are imminent."
Influential singer Peter Gabriel and classic rock acts America, Chicago and Peter Frampton are rumoured to tour in the same month.
Singer Leona Lewis is also planning shows at the end of the year.
Californian supergroup the Eagles are planning to hit Australian shores early next year, US rockers Bon Jovi plan to be here in January and seminal art rock band Roxy Music is slated to tour in February.
The line-up will include singer Bryan Ferry but not Brian Eno.
Superstar Neil Diamond is set to do a national run in March and U2 will be here in 2011.
U2's new world tour has been delayed by a back injury to singer Bono.
The Pretenders, Blondie, Hall and Oates and John Farnham are strongly tipped to do winery shows this summer.
Teen pop star Justin Bieber hinted at shows in summer but no dates are set.
Promoters are keen for singing spinster Susan Boyle, but she is yet to create a show.
The Rolling Stones' media handlers, US firm Rogers and Cowan, did not respond to email inquiries about tour plans.
But a source within the Stones said: "Keith has put the call out for a new album and a world tour."
- Herald Sun