The Chilean was sacked by los Blancos earlier in the summer after just one year in charge of the former nine-time European champions. Pellegrini, formerly at another Spanish club Villarreal, had failed to guide Madrid to any trophy in the 2009-10 campaign.
However, the 56-year-old already has a job offer. His representative has said that Pellegrini is in line to become the next coach of the Mexico national team after Javier Aguirre resigned following the 2010 World Cup finals in South Africa.
"There is an offer from Mexico and we're in conversations with them,'' Jesus Martinez told Radio Agricultura in Chile. "Mexico is a possibility."
Pellegrini had earlier been linked with the managerial post at Premier League club Liverpool, who have now appointed Roy Hodgson as their new chief.