The 22-year-old moved to Mestalla during the transfer window a year ago and made 23 appearances in La Liga last season.
Mourinho criticised Pereira for the move at the time and there was some doubt as to whether he would give the Belgium youth international a chance to impress on his return.
"It was a very important year for me at Valencia and I learned a lot," Pereira told United's official website. "I had a lot of experiences out there and I am very happy to be back. I am ready to play.
"This pre-season is very important for the team. We have to prepare very well for what is coming up next and I am doing my best to get minutes, and to show that I am ready."
Pereira suggested he expects to play as a central midfielder for United after speaking with Mourinho about his preferred position.
He is now doing his best to learn from assistant coach Michael Carrick, who retired at the end of last season after 12 years as a player at Old Trafford.
"The manager asked me what position I will play and I said I will play any position he would like," Pereira said. "Now, I am in this position as a number six. I will try to do my best and of course everyone is helping me a lot, including the manager, by telling me what to do.
"Carrick is also helping me in every training session and it is very important. It is not only them, but all of the other coaches as well. They're helping me a lot and I am learning new things every day.
"Michael was one of the best [central midfielders] in the world and one of the best that Manchester United ever had. He gives me tips, he tells me in training what to do and it is very easy when he tells you. You pick it up straight away and it is very easy to learn from him."