The 25-year-old has been with the club since the age 16 and has become an integral part of Sir Alex Ferguson's squad.
He told the Daily Star: "It's obviously an ambition I had when I was younger – I wanted to be captain of United. You look at the captains over the last couple of years, they're close to 30 before they get the nod.
"I'm sure there are plenty of players above me who want it and are in line to get it before me."
Evans has made 26 appearances for United this season in all competitions, scoring four goals.