The 19 year-old made his senior debut for Real this season under former coach Xabi Alonso.
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The Sun says Arsenal are well aware of Valdepenas' progress, with technical director Andrea Berta having seen plenty of the youngster up close during his time with Atletico Madrid.
Valdepenas can play right across the back four and his versatility is something that is attracting the Gunners.
The defender's contract at Real runs to 2029.