Asier Illarramendi swapped Sociedad for the Spanish capital in the summer, with some reports claiming that Madrid were also interested in Martinez.
Barcelona have since been linked with the centre-back, but Loren has claimed that the club have "indications" of a possible bid from Los Blancos.
"I do not know if Illarra's move can help more with how much Florentino [Perez] plans to pay. Equally we can make that effort too. Fear not," he told Mundo Deportivo.
"We must be prepared. Illarra was one of the players who were more settled here and neither he nor us thought about him leaving 15 days before he did leave.
"We have no confirmation of anything, but the front cover of a newspaper was very significant and very showy. He is a Real player and we hope that he will give his all for us, and from there we are prepared. Has there been an offer? We have had indications."
It is believed that Martinez's release clause is in the region of £25m.