Chelsea boss Graham Potter and Manchester United counterpart Erik ten Hag have condemned homophobic chanting by United fans during Saturday's 1-1 Premier League draw.
The Football Association said it would crack down on discriminatory behaviour.
"The FA strongly condemns the use of the term 'rent boy' and we are determined to drive it out of our game," said an FA spokesperson.
"We continue to work closely with the Crown Prosecution Service (CPS), as well as the UK Football Policing Unit, in relation to the use of this term."
Chelsea chose the game as an opportunity to support Stonewall's Rainbow Laces anti-discrimination campaign.