The Brazilian has struggled for game time at the Etihad this season, making just 10 Premier League appearances under Pep Guardiola.
La Gazzetta dello Sport believes that Inter have decided against making Cedric Soares' loan move from Southampton permanent at the end of the season, preferring a move for Danilo.
The 26-year-old is understood to have reached an agreement for a contract of four or five years worth €3.5 million per season.
City will not stand in the right-back's way, but want to wait until the end of the season before completing the deal.
Danilo joined the Citizens from Real Madrid in the summer of 2017 on a five-year deal but has struggled with injuries and form in England, making 33 Premier League appearances over the last two seasons.
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