That is according to Marca, who report that the 25-year-old centre-back will remain at the Santiago Bernabeu for the 2022/23 season to offer strength-in-depth in defence.
Vallejo renewed his contract with the Spanish club in 2019 until the summer of 2025.
He played just 353 minutes last season, the 23rd-most played squad member. The only two first-teamers who played less football them him last term under Carlo Ancelotti were Dani Ceballos and Gareth Bale, who will both probably leave the club this summer.
Madrid have already signed Antonio Rudiger from Chelsea this close-season meaning that they have him, David Alaba, Eder Militao and Nacho in place at the centre of defence.
Vallejo will therefore be the fifth-choice in his position.
But he is a hard worker and is popular at the training ground – one of those players that are useful to have in the squad.