Monaco, managed by ex-Chelsea boss Claudio Ranieri, wants to mark its top-flight return by making Rooney their marquee summer signing, reports the Daily Star.
Monaco officials have told Rooney's camp they are prepared to blow their rivals "out of the water" with a huge transfer fee and tax-free wage deal.
Fellow super-rich French side Paris St-Germain and German giants Bayern Munich are also keen on the unsettled England hitman, with Rooney himself understood to fancy Barcelona.
But Monaco's billionaire owner Dmitry Rybolovlev is on a mission to lead the club back to the top of European football and sees Rooney as the man to help him.
His current deal expires in 2015 and is worth a whopping 230,000-pound a week. (ANI )