The 22-year-old has been with Los Blancos since 2008, but he has only made three first-team appearances for the capital giants, and spent the 2016-17 campaign on loan with fellow La Liga side Alaves.
The midfielder impressed during his time at Alaves, and he was recalled to Madrid ahead of the new campaign.
Last week, meanwhile, respected Spanish journalist Guillem Balague claimed that Llorente could leave Real Madrid this month if he expressed a desire to depart before the close of the summer transfer window.
According to Plaza Deportiva, Valencia attempted to sign Llorente on loan at the start of this week, but were informed by Real Madrid that the midfielder had a role to play at the Bernabeu this season.
Llorente, who was born in Madrid, joined Real's youth team at the age of 13.