Tuttomercato reports that the Dutch side are looking to bolster their midfield this summer and are keen to sign Gago.
PSV sold Ibrahim Afellay to Barcelona in January and are keen to bring in a replacement for the midfield this summer.
The 25-year-old has fallen down the pecking order at Real Madrid and has long been linked with a move away form the club.
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Being an amiable guy is good for you and Jurgen Klopp is living proof.
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.