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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.