If Alves were to accept the offer, he would team-up at Shanghai with fellow Brazilians Hulk and Oscar, who signed for the club last summer and earlier in January, respectively.
The 33-year-old full back moved to the Italian powerhouse last summer, following his eight-year spell at Barcelona.
The other Shanghai club, Shenhua, signed Carlos Tevez a few days previously for a reported weekly salary of £610,000 which, if true, makes his the highest-paid footballer in the world.