The 20-year-old believes the Netherlands star is "one of the fastest players in the world" and is delighted to be able to train with him every day
Robben has been the key man for Louis van Gaal's side in the World Cup having scored three goals and picked up an assist as the Oranje beat Spain, Chile and Australia to finish top of Group B.
The Bayern Munich star's assist was for Depay himself, who slotted in his second World Cup goal in the dying minutes of his side's win over Chile and the 20-year-old is in awe of his team-mate.
"Robben is fantastic," he told De Telegraaf. "It's great to train with him every day. I can't believe my eyes how fast he can dribble the ball and I think he's one of the fastest players in the world. He's a top player and it's nice to play in a team with him.
"For my goal [against Chile] it was a great ball from Nigel de Jong and then nice play by Robben.
"Once Arjen is gone, he's unstoppable. The goal is half his. He put the ball in well and I believed I could score, so I also pointed out Arjen after the goal."
The PSV winger says he feels blessed to be at the tournament in Brazil and says the experience has made him a better player already.
"The world is very beautiful at the moment. It's nice to be playing. I've scored twice on such a big stage and I'm really happy.
"In the last weeks I've become a better player. I'm learning so much from the guys here around me. They have made me wiser."
After the World Cup, Van Gaal will begin work as Manchester United boss and Depay has been linked with a move to Old Trafford but he insists he isn't thinking about it now.
"I am still under contract with PSV until 2017 and I am now working at the World Cup. I want to stay completely focused on it."