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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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?