The Brazilian star only joined Spurs over the summer as a part of Andre Villas-Boas’ £110m North London rebuild, but is already attracting attention from the La Liga giants.
Real were linked with a late swoop for Paulinho during the last window, but were unable to beat Tottenham to his signature.
However, with the Lilywhites currently in a period of change off of the field, Los Blancos are hopeful that they can steal the enforcer away next month.
Real and Tottenham are understood to have a working relationship, which has contributed heavily to mega money deals for Luka Modric and Gareth bale in recent times.
Now the Spaniards are confident that they can use this again to lure Paulinho to the Bernabeu.
It is believed that the 25-year-old has settled well in London, but the lure of playing for one of the planet’s biggest sides may be enough to convince him to seek a transfer.
If Real are unsuccessful this winter it is likely that they will return with an end of season offer.