Carrick has only started once in the Premier League this term with Jose Mourinho opting for the likes of Ander Herrera, Marouane Fellaini and Paul Pogba in midfield.
The England international, who turned 35 in July, has instead had to settle mainly for run outs in cup competitions.
He did start United's 3-1 win over Swansea last time out and his impressive display could see him retain his place for Saturday's blockbuster clash at home to Arsenal.
But Carrick concedes that at this stage of his career, he may have to accept his future lies elsewhere.
"There's always a chance of that isn't there?" Carrick told Sky Sports.
"It is such a great club with great players, you can't take it for granted and thankfully I'm here this season and playing my part.
"Hopefully I can play more of a part in the months ahead, strive for success and try to get some sort of silverware, because winning trophies is why we are here."
Michael Carrick has sturrgled for minutes under Man United boss Jose Mourinho
Carrick has made almost 300 league appearances for Manchester United since joining from Tottenham 10 years ago.
When asked if he would like to remain at Old Trafford beyond the current campaign, Carrick said: "Yeah, but I'm 35 now and I have to be realistic.
"I'm not going to make predictions about what is going to be happening next season.
Michael Carrick in action for Man United
"We are not even at Christmas yet and I just want to play as many games as I can and see how I'm feeling, how the body is feeling.
"That is the biggest gauge to see if I can still do it, if I feel I can still do it and the manager feels that.
"There is a lot of things to come into the equation, so I'm not going to be making any rash judgements just yet."
dailystar.co.uk