Pep Guardiola sought out Fred after the Manchester United midfielder found himself at the centre of a racism storm on Saturday, sources have told ESPN FC.
The Manchester City manager spoke to the Brazilian after concluding his media commitments following United's 2-1 win at the Etihad Stadium.
The club's chief executive, Ferran Soriano, also spoke to United director David Gill in the tunnel after the final whistle.
Pictures appeared to show a fan making a gesture towards Fred and teammate Jesse Lingard in the 67th minute of the Manchester derby.
Greater Manchester police have confirmed a 41-year-old man has been arrested on suspicion of a racially aggravated public order. Sources have told ESPN FC that City will issue a life ban for any supporter found guilty of racism.
Defeat to United saw City slip 14 points behind leaders Liverpool but Guardiola insists he will not throw in the towel to focus on the Champions League.
"We are not thinking to win the Champions League in that position," said Guardiola.
"We are trying to win games, to win the next one. I am not thinking about how many points we need or how many points they have to drop.
"We are not able to be consistent like we were in the last two seasons so that is the reality and you have to help the players."