The 21-year-old is widely regarded as one of the best talents in Spanish football, but has been used sparingly from the start by Los Blancos this season.
The striker's current deal expires in 2015, with a number of European clubs believed to be monitoring developments at the Bernabeu.
"Could Inter Milan step up their interest in him? I won't rule it out, it is a possibility," Juanma Lopez told calciomercato.com.
"Will he play for Inter next season? It could be, anything could happen. There's no news on a Real Madrid contract renewal."
Morata recently claimed that he feels 'privileged' to be at Madrid.