The 26-year-old has become one of Ole Gunnar Solskjaer's most trusted players this season, featuring 33 times in all competitions.
United also have an FA Cup fifth-round clash with Derby County to come next week and Fred is keen to go all the way in both competitions.
"I'm playing well and getting better every day," he said in an interview with United People's TV.
"I want to be a big player and be part of the history at Man United.
"I came here because it is a big club, so as I said I want to win trophies, continue to work hard and make my name here at Man United."
Next up for United is a trip to Everton in the Premier League on Sunday.