"Roy is on a list of possible signings we are discussing," Real communications head Antonio Garcia Ferreras was quoted as saying by BBC Sport on Monday.
Ferreras also played down rumours hinting that the Ireland international already passed a medical examination and said that they were still studying the deal.
"Nothing has been decided so far and he has not passed a medical, nor will he do so in the next couple of days, What is true is that the player was offered to the club around a month ago and because of his characteristics he is the sort of player that interests the technical staff.
"They are going to sit down in seven or eight days and decide on who, if anyone, the club will sign when the transfer window opens," Ferreras added.
The 34-year-old is expected to be offered a six-months deal at Real, which will include the option of expanding the contract in the case that his move proves successful.