The former Barcelona boss is prepared to start Chelsea goalkeeper Kepa Arrizabalaga against Bosnia on Sunday, according to AS.
While De Gea has been incredible for his club side, in recent seasons, his form for the national team has been poor.
De Gea was widely criticised in his homeland during a disappointing World Cup outing earlier in the year.
The goalkeeper made another error on Thursday when he parried the ball into the path of Tin Jedvaj as Croatia sealed a 3-2 victory against Spain.
It marks the second competitive match in succession that De Gea has conceded three goals for La Roja.
AS reports that Enrique has told De Gea he no longer has his unwavering support.
He told De Gea he will give Chelsea record signing, Kepa the chance to impress against Bosnia and Herzegovina.
Kepa is expected to start in Las Palmas against Bosnia on Sunday and could put serious pressure on the No.1 jersey if he impresses.