The midfielder's current deal is due to expire at the end of the season, but Carrick, who pulled out of the latest England squad with groin injury, is keen to remain at United.
Carrick arrived at United in 2006 from Tottenham and has gone on to make 361 appearances in all competitions for the club, winning five Premier League titles and the UEFA Champions League.
Injuries have meant that he has only featured twice under Louis van Gaal this term, but he hopes to impress enough to earn a new contract.
"My contract is up at the end of the season," he said. "I want to stay, of course. I've got nowhere else to go."
"They [discussions] have not really [started], not yet.
"But I haven't expected [that] to be honest, with the injury. It will probably around Christmas or after that."
Carrick, who had only just returned from an ankle injury, hopes to be fully fit for United's trip to Arsenal on November 22.
