Robben has been regarded by many as one of the players of the tournament and scored three goals for his country as they qualified from the group stages.
Depay has also made an impact in Brazil, and became the youngest Netherlands international to score at the World Cup when he found the net in their 3-2 win over Australia.
The 20-year-old has admitted that he is enjoying the experience of training with a player of Robben's standard and has been particularly impressed by the winger's pace.
"Robben is fantastic," Depay told reporters.
"It's fantastic to train with him every day. I can't believe my eyes what he can do with the ball. It's unbelievable how fast he is with the ball. He's a great player."
The Netherlands will face Mexico in the last 16 of the World Cup on Sunday.