Manchester City boss Pep Guardiola sought out Manchester United midfielder Fred after Saturday's derby defeat.
Fred was subjected to alleged racist abuse during Saturday's Manchester derby.
ESPN says City boss Guardiola approached the midfielder inside stadium to discuss the episode after he had concluded his post-match media commitments.
A conversation between Ferran Soriano, the hosts' chief executive, and United director David Gill also took place in the tunnel following the final whistle.
A 41-year-old man was arrested by Greater Manchester Police on Sunday on suspicion of racially aggravated public order after an investigation was launched.