The Football Association has written to Manchester City to ask the club for its response to a tweet sent by midfielder Bernardo Silva.
The anti-discrimination charity Kick It Out had earlier called on the FA to act after the governing body confirmed it was investigating.
Manchester City declined to comment.
“We are extremely disappointed to see the tweet posted by Bernardo Silva,” said the anti-discrimination body.
The post was published at 12:44 BST on Sunday but was deleted at 13:30.
Bernardo then tweeted: “Can’t even joke with a friend these days.”
France defender Mendy and Silva are close friends and played together at Monaco before both joined City in 2017.
Mendy responded to the tweet and did not appear to take offence. A previous video of Silva joking with Mendy has also been passed on to the FA.
A Kick It Out statement added: “Racist stereotypes are never acceptable as ‘banter’, and we’re shocked that someone who is a role model to millions has failed to understand the discriminatory nature of his post.
“The FA has been notified and we believe that retrospective action should be taken, including mandatory education – which is vital to challenge offensive behaviour such as this.”