The 19-year-old USA international has emerged as an alternative option to that of Eden Hazard, with it not be clear whether Chelsea are prepared to sell their star man to Los Blancos.
Pulisic, who is valued at around £60 million (Dh288m), has no shortage of admirers as Liverpool and Bayern Munich have also revealed their interest in the rising star.
Whites president Florentino Perez wants the club to continue their transfer policy of signing fledging youth players, like they have done in the summer window with the acquisitions of Brazilian Vinicius Junior and 22-year-old full-back Alvaro Odriozola from Real Sociedad.
