The 20-year-old was one of the players along with captain and central defensive partner Richard Dunne, in transfer speculation after City sacked Sven-Goran Eriksson.
However, Hughes, who left Blackburn to join City, seems to have succeeded in persuading Dunne to stay, while Richards is also readying for next season.
The England international, who is preparing for the pre-season training after undergoing a surgery for the knee cartilage problem towards the closing stages of last season, said on the club's official website: "We've got a new manager now and he did a great job at Blackburn and hopefully he can do the same with us.
"I first spoke to him briefly when I was in last week and he seems like a very good guy. Everyone appears to respect him and that's the main thing.
"It's impressive that he's gained that much respect straight from the start from the other staff and he'll certainly command that when the rest of the players return to training."