Richardson has made just two substitute appearances for The Whites, but is keen to continue playing first-team football.
"I am just going to take it as it comes and see what happens," the 21-year-old told the Stoke City official website.
"I'm really enjoying it at City, but then again my dream has always been to break into Leeds' first team.
"But I know that playing well here will stand me in good stead to do that whenever I go back to Leeds."
