The centre-back sent a message in response to a tweet posted by Massadio Haidara, who joked about Taylor's attempts to learn French.
The 27-year-old Greenwich-born defender replied to Haidara with a tweet that included photographs of four black stereotypes, and mentioned the names of fellow team-mates Moussa Sissoko, Papiss Cisse and Vurnon Anita with a message which read: "It's always good to see you guys smiling."
Although Haidara described Taylor's tweet as "banter," it angered a number of people on the social networking site.
Taylor, who stressed that his original tweet was meant to be taken as a joke, later sent another message saying: "Apologies if my tweet offended anybody."
However, he could still face disciplinary action from his club and the Football Association.
Apologies if my tweet offended anybody.- Steven Taylor (@27StevenTaylor) November 15, 2013
@27StevenTaylor Is Just Bander with Papiss , Moussa , Vurn' and Me . He joke with me 2 min before .- Massadio Haidara (@MassadioHaidara) November 15, 2013