However, the Spanish FA and its new president Luis Rubiales are understood to be furious with the way Lopetegui has handled the situation, prompting him to fly back from the FIFA congress in Moscow to Krasnodar, where the Spain team are based.
The Independent reports that they are considering a change of manager, with a press conference later today expected to clarify Lopetegui's position.
The 53-year-old is unbeaten in charge of Spain since taking over following their Euro 2016 exit, and La Roja are regarded as one of the favourites to lift the World Cup trophy in Russia this summer.
However, Rubiales reportedly feels betrayed after only finding out about Lopetegui's Madrid agreement five minutes before it was announced by Los Blancos.
Spain sporting director Fernando Hierro and Under-21 coach Albert Celades are regarded as the main candidates to take over should Lopetegui be sacked, although Rubiales may feel that it is too late to make a change considering Spain get their campaign underway against Iberian rivals Portugal in Sochi on Friday.