The Chile international has endured a tough time at Old Trafford since moving from Arsenal last January, as Henrikh Mkhitaryan moved the other way.
The 30-year-old has only scored three goals in 29 Premier League appearances, having struggled to perform under Jose Mourinho and then caretaker manager Ole Gunnar Solskjaer, leading to speculation that United are already considering ways to offload a player who reportedly earns a basic salary of close to £350,000 per week.
Sanchez suffered knee ligament damage in the 3-2 win over Southampton this month and is not expected to be fit until at least the middle of April, prompting suggestions he could have played his last game for the club already, but the forward is determined to triumph.
"Obviously, I want to make the United fans really happy," he told Inside United magazine prior to his injury. "I want to score goals. I want to bring them joy. I want to win silverware.
"When we lost last year's FA Cup final to Chelsea, I was not happy. Not happy at all. In fact, I was sad because I just wanted to make our wonderful supporters happy. I saw the fans who had come to pack out Wembley Stadium. They were all around me – all red. I liked it. Wembley was all red.
"The goal there [at Wembley] against Tottenham comes to mind. It was such a great moment because the United fans were right on top of us and it was a lovely moment to be able to celebrate along with them.
"When I was younger, I liked United. I swear. As a small child, I liked United. I really liked them. And I want to show this and bring the people joy because, obviously, I want to win.
"I want to keep showing my love for football. 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."
Sanchez's finest form came in an Arsenal shirt, where he impressed consistently under Arsene Wenger after joining from Barcelona in 2014.
Born in Tocopilla in northern Chile, Sanchez admits he never imagined he would enjoy a successful career in Europe.
"It's a small city," he said. "Listen, I love football. I love football! My passion is football. My other passions are my dogs and my family. They mean everything to me. Everything. Growing up, I always wanted to be a professional footballer – but in Chile. Always in Chile. I never dreamed of coming here to Europe. Never.
"It was always the Chilean league for me but my footballing journey continued and I played in Argentina and Italy. After that, I was like: 'Wow, this is football! I love football!"