If the transfer goes through it is likely to mean City's out-of-favour England goalkeeper Joe Hart will leave the club in a loan deal or a permanent move.
Bravo made 32 league starts last season to help Barca win La Liga and featured in Saturday's 6-2 rout of Real Betis.
"We have a preliminary agreement with Manchester City for the transfer of Claudio Bravo," technical secretary Robert Fernandez told the club's TV channel.
"But before we open the door we have to sign a goalkeeper."
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(Reporting by Adriana Garcia; Editing by Tony Jimenez)
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