Fabio says he is willing to scrap with his brother Rafael for the right-back slot in David Moyes' first team.
The Brazilian, who made his first competitive start under the manager in the 2-0 win against Crystal Palace, is desperate to grab the opportunity presented by the injuries to his twin and Phil Jones.
Following an assured display in Saturday's victory, the South American defender is targeting more involvement on the back of last season's loan spent at QPR.
"I think I did okay today," he told PA Sport. "I definitely want to impress the new manager. I did this on the training ground. That is why I played today. I trained hard. I worked hard. He has seen me do that on the training ground, so he put me in the team. Hopefully, if I play well, I will stay there and I will fight with my brother for the position.
"That is what I have spoken about with him in the past. Now we are going to fight with him for the position. Why not? We have always fought over everything - PlayStation, anything.
"We fight with each other to win. This is no different. Now we are 23. We are mature. It is important, whether me or him plays, that we do well.
"I am confident in myself that I can play for Manchester United. But Manchester United is one of the biggest clubs in the world. They have fantastic players here.
"If it doesn't work out here maybe I have a chance of going to another club but I am still hopeful of playing here. I will try to the end to do that. I got in the team today and hopefully I can play more throughout the season."
More: Moyes praises Rooney | Manager's verdict on Fellaini