His initial deal is set to come to end following Forest's Championship clash with Cardiff on New Year's Eve.
"We're trying to sort something out with Greg," Cotterill told the club's official website. "We would hope to find out whether it's possible before the Cardiff game.
"We think Manchester City are happy with his progress here. He's getting to play first team football at a very good club and City know that.
"I've had a couple of conversations with David Platt and we've obviously spoken to Greg, who is very happy here. He really likes it.
"I've also spoken to Greg's agent, who I know really well. It's always a bonus when you know the player's agent and have a good relationship with him."