The 29-year-old moved to Old Trafford during the January transfer window in a swap deal which took Henrikh Mkhitaryan in the opposite direction to Arsenal.
He has committed to a four-and-a-half-year contract with United and will be 33 by the time that agreement comes to an end.
Sanchez has suggested that there is little chance of him extending that stay, with there a desire on his part to head home before slipping into retirement.
He told Chilevision: “I think it would be my family's dream.
“My father who is now in heaven was a supporter of La U and I think the truth is that a lot of my family would like me to end up there.
“My dad was the pillar of the family and sometimes people do things for their family as well.
“I played for Colo Colo and the truth is that it was great and I won a lot of things with them, but I think people are going to understand it because it’s a dream my dad had and god willing I am going to fulfil it.”
Sanchez has, however, suggested that he would like to work in the Premier League again at some point further down the line, with English lessons intended to help him into a future coaching career.
Those plans must wait for now, though, with the present very much about United.
A move to the Red Devils was made as Sanchez ran down his contract at Arsenal, and the highly-rated forward admits that the Gunners did all they could to keep him before reluctantly sanctioning a switch.
He added on discussions with a former manager at Emirates Stadium: “Arsene Wenger was very fond of me. He told me: ‘I want you to stay because you are the best player in this team.’
“However, I wanted to continue growing as a player, more so as a Chilean, because it’s difficult to get to Manchester United. No Chilean had played here.
“Arsene understood it at last, we ended up on good terms, he congratulated me and there was no problem.”