Bernardo is set to leave City when his contract expires at the end of the season and is in contact with Juventus.
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However, Sport says the 31 year-old's agent, Jorge Mendes, is currently in contact with Barca powerbrokers about taking on his client.
Bernardo was priced out of a move to Barca two years ago by City and has hopes of reviving negotiations now that he is available as a Bosman transfer.
Mendes is working on Barca coach Hansi Flick and sports director Deco about signing the midfielder, despite his likely high wage demands and also the depth of midfield options available to Flick.