The Argentina defender has not featured for Louis van Gaal's side since December 8 due to a thigh injury, but he revealed to United Review that he is closing in on a return.
United face Stoke City in the Premier League on New Year's Day, before travelling to Yeovil Town in the FA Cup three days later, and Rojo – who has made 10 appearances for the club - hopes to get some game time to build up his match fitness.
He said: "Certainly there are a lot of games coming quickly, one after another. That's what I want, to get fit as quickly as possible so I can lend a hand to the team.
"The manager is going to want as many players as possible for this busy period. It's an important part of the season with so many games in quick succession.
"I've had the misfortune to get injured recently and I really don't like it. It's terrible to miss training and be out of the team.
"I just hope I can regain my full fitness quickly and it doesn't happen again, as it's never good being injured."
It is the second spell on the sidelines for the 24-year-old since arriving at Old Trafford in the close season, having previously suffered a dislocated shoulder in November.
