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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.