The 25-year-old previously endured loan spells at Royal Antwerp and Sunderland but has been a first-team regular at the Red Devils for the past 18 months, having progressed through the club's youth system.
The Northern Ireland international, who signed a new three-and-a-half year contract in December, says that he wants to end his playing days at the club.
"When I was younger, clubs were asking me to go on trial from a young age and I never went on trial to another club," Evans told Inside United.
"I just knew that Manchester United was the place I wanted to play football.
"So to play here throughout my career would be something I would look to do and I'd love to do it."
United host Fulham in the FA Cup on Saturday.