Former Old Trafford favourite Nicky Butt and ex-Arsenal striker Alan Smith made the draw, as the Reds' number 13 came out with the current Barclays Premier League leaders.
"We want to progress as far as we can and will do our best to try and do that," Sir Alex told Sky Sports earlier. "Winning is always important at this club."
"You've got to beat the best teams to win the cup," said Tom Cleverley after the draw.
"Obviously we would have preferred a home match because you don't want to travel too much in a busy fixture list but whoever plays for us will go down there to Chelsea and do their stuff."
The ties will be played in the week commencing 29 October, so the Capital One Cup meeting will come just two or three days after the rivals meet in the league at Stamford Bridge.
Full fourth round draw: Sunderland v Middlesbrough, Swindon v Aston Villa, Wigan v Bradford, Leeds v Southampton, Norwich v Tottenham, Liverpool v Swansea, Chelsea v United, Reading v Arsenal.