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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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.