"It's 90 percent certain," he told Sportv in his homeland. "It just depends on a few bureaucratic details."
The deal would cost the Chinese side a reported 60 million euros (50.26 million pound) according to media reports and bring him under the tutelage of Andre Villas-Boas, a former Chelsea coach who tried to sign him while in charge at Tottenham Hotspur.
Fellow Brazilians Hulk and Elkeson play for Shanghai.
A spokesman for the Chinese club would not comment on the reports.
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Oscar joined Chelsea in 2012 and has won the Premier League, Europa League and League Cup with the London side.
But after starting the first five league games of the season under new coach Antonio Conte, he has fallen out of favour and been used only four times as a substitute since September.
The progress of Gabriel Jesus and Philippe Coutinho have also limited his international chances and he has yet to appear for the national side under new Brazil coach Tite.
(This corrected version of the story makes clear in paragraph three Oscar has not played under Villas-Boas.)
(Writing by Andrew Downie; editing by Ken Ferris)
