The Manchester United goalkeeper has been questioned over his passing abilities this season as Ten Hag looks to build attacks from the back.
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But he has often underwhelmed with the ball at his feet, as shown in United's 4-1 win over Real Betis at Old Trafford on Thursday night.
One pass in particular almost led to Betis taking the lead just before the break, with Red Devils legend Paul Scholes subsequently hitting out at the 32-year-old's distribution.
The BT Sport pundit said: "David isn't the best footballer let me put it that way. Very strange pass."
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And Ten Hag has stated that he cannot turn a blind eye to his errant kicking, though he offered an explanation as to why his passing wasn't up to scratch.
He stated: "From today I can't ignore it, but I think we have seen many games he did really well.
"I don't know what the reason was. There was a lot of wind, a different ball, probably he had some problems with that.
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"But I know we can deal with it and he will do better Sunday [against Southampton].
"We work on that but David is working on that.
"But I think we have seen in this season that he is improving and he will keep improving, I'm sure."
De Gea is facing an uncertain future at the Theatre of Dreams with his deal to expire in the summer, though United have the option of triggering a one-year extension.
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Though it has been claimed that United are keen to offer him a new long-term contract, though he will have to take a pay cut on his £250,000-a-week salary.
But it is believed that United will look to sign another shot-stopper at the end of the season, with Leeds' Illan Meslier a potential option.
Meanwhile club icon Gary Neville has named Brentford's David Raya as a possible long-term successor to De Gea.
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Speaking on The Overlap earlier this month, he remarked: "I think Raya would interest United in the summer.
"I went to watch Brentford on a Saturday a couple of weeks ago. I think he's going to become available, he's only got a year left.
"I think he could step up."