Fernandez filmed himself and several Argentina teammates singing a derogatory song about the French national team, referring to them as Africans despite nearly all of them being born in France.
However, the Press Association states that Chelsea have accepted Fernandez’s apology to several of his French team-mates.
Blues manager Enzo Maresca had played down any rift between the players due to the issue.
Chelsea have several French players who are black or mixed race, including Axel Disasi, Benoit Badiashile, Lesley Ugochukwu, Christopher Nkunku, Malo Gusto and Wesley Fofana.
The latter claimed Fernandez demonstrated uninhibited racism" by signing the song and posting it online.
