The Spaniard has impressed in recent weeks in games against Ajax, Liverpool and Chelsea and his team-mate believes he can only continue to improve.
Evans told reporters: "Now his presence is building. The language barrier is being broken down and he is coming out of his shell a bit.
"He has a joke now and is not afraid of getting involved in some of the dressing room chat. That is settling him down."
The Northern Ireland international also suggested that De Gea had actually benefited from the language barrier during the first half of his first season, particularly after he came in for criticism due to some high profile errors.
"Probably it was a good thing David couldn't speak English at the start. It seemed like he was coming into training and nothing was affecting him. He was just getting on with his game," added Evans.
"But it was because he couldn't read or understand what was going on around him. Overall, that was probably better."
Evans also spoke highly of his team-mate's abilities and believes he has shown real character in recent weeks after a difficult start to life at Old Trafford.
"David had a big price tag when he came to us during the summer. People had these huge expectations. From day one, his shot stopping has been unbelievable. He pulls off saves that are amazing," said the defender.
"He just needed a bit of confidence. I am sure everyone at Manchester United has been through stages when it has not gone well. Then it is down to your character to pull you through."
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