Moyes will officially succeed the recently-retired Sir Alex Ferguson on 1 July and, during a short interview with Spanish media, De Gea was quizzed on the high-profile changing of guard at Old Trafford.
"It was a surprise to us all that Ferguson left," David explained. "But we know that when we get back to training he [Moyes] will be there and it is going to be a pleasure to work with him."
But De Gea isn't thinking too much about next season yet. He knows there is plenty of work to do with Spain at the Euros before then.
The 22-year-old has played every minute of the competition thus far, keeping two clean sheets in wins over Russia and Germany to secure a semi-final place ahead of Wednesday’s Group B decider with the Netherlands.
“It was very important,” David said of Spain’s 1-0 win against Germany on Sunday. “We are into the semi-finals again and we are very happy with that.
“They are all good teams when you get to this stage of a tournament; they all have a lot of quality. It will be difficult whoever we face.
“We have had two tough games and, thankfully, we have been lucky enough to get through.”
De Gea is also hoping to claim back-to-back European titles after winning in Denmark two summers ago. It's a plan that contrasts starkly with the endeavours of England, who exited both tournaments at the group stage – a fact that shocked the United starlet.