The Argentine, 24, chose the R's ahead of offers from Spain and Italy when moving to England two years ago.
QPR's Italian adviser Gianni Di Marzio has revealed Real have made inquiries.
Former Napoli coach Di Marzio told Calciomercatonews: "Several clubs have asked for the Argentine Faurlin. He is a 25-year-old midfielder.
"For him, even Real Madrid have come forward."