Concise News learned that Wright spoke on the back of the Spain international’s poor form, lately.
De Gea‘s mistake allowed Chelsea to equalise in Sunday’s 1-1 draw at Old Trafford.
But Solskjaer backed the United number one to shake off his poor form in their final two games against Huddersfield Town and Cardiff City.
However, Wright believes the Norwegian has to take a different approach.
“If he [Solskjaer] really wants to stamp his mark and let people know he isn’t afraid to make decisions, he should take him out,” Wright said on BBC Radio 5 Live.
“If the manager explains everything and tells him face to face why he’s leaving him out and giving him a break, that’s man-management and that’s what Solskjaer has to do.”
Wright said an early end to De Gea’s season would help the struggling Spaniard sort out his future at the club, while back-up Sergio Romero fills in.
The former Arsenal forward added that “He (De Gea) needs to go on holiday and sort his contract out,” Wright added. “Sometimes you have to take someone out the firing line. He’s one of the best goalkeepers in the world and he needs a break.
“There’s a lot going on and he’s under a lot of pressure. When you look at how United are playing at the moment, putting him in that situation is putting him under more pressure.”