The centre-half is out of contract at the end of the season with talks continuing over his future.
The report adds that the player could be looking for one final big payday and that might not be at Real Madrid who are hopeful of reducing their wage bill.
According to AS PSG will offer a three-year deal worth £18m per season after tax.
But there are also reports that Manchester United are ready to make their move.
Ole Gunnar Solskjaer would no doubt jump at the chance to bring into his side an experienced, top-quality centre-back and leader.
But if contrary reports are to be believed, all is not over for Ramos at the Bernabeu.
As reported by El Chiringuito, Ramos ‘has an agreement’ with club president Florentino Perez of a two-year deal worth £10m a season.
There will even be the option of a third year, that would take him past his 38th birthday.