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.