The club's representatives have already talked with the 25-year-old Brazilian about his possible transfer.
Brazil's Palmeiras is also interested in the player. Bernard's contract with the Ukrainian club ends next summer, so he can sign a preliminary contract in January.
Bernard has played for Shakhtar since 2013, scoring 27 goals in 151 matches and winning six titles, including two in the national championship.
In the winter of 2015, Jiangsu Suning signed another Shakhtar midfielder, 27-year-old Alex Teixeira, who may move to Inter.
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