Cadena SER report that Florentino Perez is keen to sign the duo, both of whom are likely to leave their clubs this summer.
However they may face a challenge to win the race to sign both, with Isco possibly joining his manager Manuel Pellegrini in moving to Manchester City, and Lewandowski likely to go to Bayern Munich.
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Who of Europe’s top strikers will move to England this summer?
After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.