Centre-back Taylor became embroiled in a Twitter storm after he mocked four of his black team-mates.
The tweet, aimed at Massadio Haidara, Moussa Sissoko, Papiss Cisse and Vurnon Anita, featured pictures of three black stereotypes and one of Anita.
In addition to the controversial image, Taylor wrote: "It's always good to see you guys smiling."
Taylor has since apologised for the incident, but the FA have now confirmed to Perform that they are looking into the matter and have given the defender until Wednesday to respond.
Newcastle were unavailable for comment on the subject when contacted.
The FA have previously taken a hard line on players' behaviour on social media, with Rio Ferdinand fined £45,000 in August 2012 for using the term 'choc ice' on Twitter.
