The Red Devils are currently getting to grips with their new manager’s methods following his arrival at Old Trafford in May after the sacking of Louis van Gaal.
Mourinho has plenty of experience in the Premier League with Chelsea and has guided the Blues to three top-flight titles during his two spells with the west London club.
Manchester United have struggled to challenge for trophies since Sir Alex Ferguson opted to retire at the end of the 2012-13 season.
The Red Devils ended up fifth in the top flight last season despite winning the FA Cup under Van Gaal.
However, goalkeeper De Gea feels that United have the right man in charge to take the club forward this season and beyond.
Speaking in an interview with Sky Sports before Monday’s game at Liverpool, De Gea said: “I think it’s the most competitive season in the Premier League. A lot of teams are really good and fit, but we are United, we like this challenge and want to fight for the league.
“Jose is a manager who has a lot of Premier League games in the bag and he speaks with us all the time in the big games to motivate us and try to win every game.
“We have a great team with the new players, they are really good and we need to show and fight for every ball, every game and try to play our best football.”
Manchester United travel to Chelsea on Sunday.
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