Fernandes, 26, has been the club's standout performer since joining United from Sporting Lisbon last year for an initial fee of €55 million, contributing 24 goals and 14 assists in all competitions this season.
However, the Portugal international has outlined his coaching ambitions after hanging up his boots and wants to test himself at Old Trafford.
"I'm trying to enjoy the football, you know. I think I want to be a coach," he told the club's official website. "Honestly, I would like to be a coach. I don't know which team I would like to manage.
"Of course, the biggest team if I can manage Manchester United, I will be happy. I can leave now just some words so if people see this, if I'm a manager in the future, the fans can make some pressure to bring me as a coach.
"But I think I would like to be a coach in the future. I'm not sure but for what I feel for football, for the feeling I have, I think I have to continue to be inside of football because my whole life is about this. So I think, in the future, it needs to be with football too."
United have failed to progress past the semfinal stage in their last four attempts in three different competitions under Ole Gunnar Solskjaer but Fernandes said the team are getting better with the Norwegian at the helm.
"I think, honestly, the team has improved a lot since I arrived," he added. "I feel the improvement but I think the team is improving since the coach arrived. He's trying to put his hand on the team and make it better and better."