De Gea endured a difficult start to his Old Trafford career following a €21 million move from Atletico Madrid in 2011, with inconsistent displays leading to speculation over his short-term future as the club's first-choice shot-stopper.
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"[The defence] have all improved,” Sir Alex said ahead of Monday night’s showdown with Manchester City. "The concentration has become better and the importance of the games has helped that.
"But David de Gea has developed and matured as the season has gone on. Once again he had an excellent game the other day at Stamford Bridge. We've seen a very progressive and developing young goalkeeper and next season he'll be even better."
And the 22-year-old - who has kept clean sheets in each of his last six Premier League games - has adapted well to life as a Manchester United player, according to defensive partner Rio Ferdinand.
"You have to get used to it. You need a thick skin to be a Manchester United player," Ferdinand added. "Because if you cannot take a battering at times you will fall by the wayside and someone else will fill your shoes.
"He has a huge price tag on his head that carries a lot of weight. But he is resilient, even if he still has a lot to prove because this season is not over yet."