The Spanish champions are known admirers of Fabregas and the Arsenal midfielder was one of president Ramon Calderon's transfer pledges when he was running for election last summer.
Real were unable to bring Fabregas to Madrid at that time though, and they also failed in their bid to sign the 20-year-old this summer, with the player committing his immediate future to Arsenal.
However, it could be third time lucky in 12 months' time, with Calderon hinting they will be making another bid for the Spain international, who came through the youth ranks at Real's arch rivals Barcelona.
When asked if there was still time to sign the three players he promised during his election campaign - namely Arjen Robben, Fabregas and Kaka - Calderon said: "There's a chance that they will all be here by the end of my third year in office."
And when queried if that could mean Robben this summer, Fabregas next year and Kaka the following year, Calderon told newspaper La Razon: "Well yes, I think so. I don't want to create any false expectations."