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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?