The purported world-record deal for the 31-year-old comes after he broke Sir Bobby Charlton's long-standing record to become United's all-time leading goalscorer with a last-minute equaliser for his side at Stoke City on Saturday.
According to The Sun, an unnamed Chinese side is currently preparing the offer, which would dwarf both Rooney's current £300,000-a-week wages and the world-record £615,000 a week earned by Carlos Tevez after he moved to CSL outfit Shanghai Shenhua in December.
"There is a belief that Rooney might be allowed to leave United this summer, by which time he'll have spent 13 years at the club and made more than 550 appearances," a source told the newspaper.
"Even though he'll have one year left on his contract, it's a good time to go because he is now the top scorer in the club's history. He would probably sign a two-year deal in China and will earn more in that time than he has done during the whole of his United career.
"It will be a big wrench for him and Coleen and their boys because they are very settled in Cheshire and Coleen in particular is very close to her family. The boys are happy at school. But they both know a footballer's career is a short one and it would be silly for Wayne not to maximise his earning potential, especially as he's approaching the latter stages of his career."