The left-back has been at the club for seven years but is still waiting to win the trophy, despite having collected medals from the Premier League, Champions League and Capital One Cup during his time at Old Trafford.
"The boss has given a big message this season – he really wants to win the FA Cup," Evra told United Review ahead of Saturday's fourth-round clash with Fulham. "He really wants it and so do we."
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"It is the only trophy that I have not won at Manchester United," Evra added. "That seems impossible given that I am now in my seventh year here. The FA Cup means so much and, one day, I hope I will win it. Hopefully this year."
The defender believes that there is enough depth in the squad to enable them to compete for the trophy while maintaining their form in the Premier League and Champions League.
"Manchester United is the only team that can make 10 changes and still win," he claimed. "You might hear people call it a 'second team' but it's not.
"Everyone is a United player and you trust each one of your team-mates. The manager makes those changes because he trusts that we are going to win. He's not crazy, he knows exactly what he is doing."