De Gea played alongside Carrick for several years at United.
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In England for Fiorentina's Europa League quarterfinal first-leg defeat at Crystal Palace on Thursday, De Gea was asked if he was following the impact Carrick was making as United manager.
"He's doing unbelievable," De Gea told TNT.
"He's a great guy, he knows how the players feel, so it's easy to talk with him. He's doing an amazing job, United is winning a lot of games now, playing well.
"Hopefully we can get the Champions League spot and keep growing, growing, and let's see United again in the high positions and fighting for trophies."
For the moment, Carrick is contracted to the end of the season.