The Chilean has failed to live up to his lofty standards since joining United from Arsenal in January 2018, scoring just five goals in 41 appearances for the club.
A number of clubs have looked at signing the club's highest earner, but Sanchez says he wants to stay at Old Trafford and win silverware.
"I want to keep showing my love for football," said the South American.
"I know what I can do. I have belief in my ability.
"United are such an important club, not only in England but on a global level, and I would love to help bring a trophy to the supporters."