The 21-year-old, who enjoyed a breakthrough season at the Bernabeu last term having spent time out on loan with Real Zaragoza and Eintracht Frankfurt in the previous two campaigns, is not assured of regular first-team action under new boss Julen Lopetegui.
That has led to reports Vallejo could return to Germany’s top-flight again, but this time on a permanent basis with Hoffenheim.
The player himself is thought to want to stay in the Spanish capital and fight for his place, though he may relish the chance to work with highly-rated Julian Nagelsmann.