The 18 year-old defender is a regular with Alvaro Arbeloa's Castilla team. He has a deal to 2029.
Transfer expert Fabrizio Romano is reporting on his YouTube channel: "Who could be the next talent to play for Arsenal? I have a name. It is a talent that Arsenal have been following for a few months now and it is a player they continue to look at.
"It will not be easy at all because he is a Real Madrid player, his name is Victor Valdepeñas, also called Valde. He is considered an important talent, a very young player from the Real Madrid sector.
"He is a Real Madrid player and we know very well how difficult it is to sign players from Real Madrid because all the players want to stay at Real Madrid and see it as the best possible project. So it is not easy, but Arsenal have definitely followed and monitored this guy."