Shanghai are managed by ex-Stamford Bridge boss Andre Villas-Boas.
Oscar hasn’t been a starter for the Blues in recent weeks.
He’s had to settle for a spot on the bench during their run of nine straight Premier League wins.
But should Chelsea cash in on the Brazilian ace, or keep him on board to boost their title challenge?
Have your say in the poll below.
Oscar joined Chelsea from Internacional in July 2012.
Villas-Boas had been given the boot by the west London club by that point after his miserable spell in charge.
But he could yet work with the player if Chelsea sanction his departure.
The Guardian report an offer has been made by Shanghai, and the Blues are willing to sell.
Rival Chinese clubs Jiangsu Suning and Guangzhou Evergrande are also said to be after Oscar.
Another escape route for the player could be to Italian giants Juventus.