The young left-back recently earned his first England cap, and the Saints boss believes that he has the talent to turn out for the nine-time European champions.
However, Pochettino said that he will not discuss Shaw's or his own future until the end of the season.
Pochettino told reporters: "He can play at Real Madrid or in the world starting XI. He has the quality to do so.
"I'll repeat what I said exactly last week. Everything is calm and we are working to finish the season off as best as possible."
The Saints are currently ninth in the Premier League.