The Portugal midfielder now has until Monday, October 21 to respond following an application made to the chairman of the judicial panel.
Silva, who originally had until Wednesday, October 9 to answer the charge, could face a six-match ban due to the racist connotations of the image he posted to his team-mate.
Silva tweeted a picture of a childhood Mendy alongside one of the brand mascot of Spanish confectionery brand Conguitos on September 22.
After criticism, he deleted the post before adding a second tweet that said: “Can’t even joke with a friend these days… You Guys…”.
Sky Sports News understands that Silva wrote a personal letter to the FA after the governing body made contact with City to seek their observations as part of the investigation.
The letter was supported by a statement issued by Mendy himself, who declared he had not taken any offence over the social media post.
City boss Pep Guardiola also defended Silva on two occasions over the incident, calling him an “exceptional person”.