The defender, 34, comes off contract in June and is now free to commit to a pre-contract with any foreign club.
According to El Chiringuito's Josep Pedrerol, Ramos met with Florentino and informed him that he does not intend to accept the offer to renew, instead making himself "available to listen to proposals from other clubs".
Ramos even told Florentino: "At PSG, I was told that they will make a team with me and (Lionel) Messi".
Like the Real skipper, Messi's contract with Barcelona also ends in June and remains at odds with the board about talks over a new deal.
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