It is an awkward time for Jose Mourinho's side after a 0-0 draw at Deportivo La Coruna last weekend and Chilean Pellegrini would like nothing better than to add to their woes.
He was fired at the end of last season having failed to win silverware during a year in charge and was replaced by Mourinho, fresh from leading Inter Milan to an unprecedented treble.
However, they still finished second to Barcelona, were humiliated in the King's Cup by third-tier Alcorcon and slumped out of the Champions League in the first knockout round.
However, they have been struggling for most of the campaign and only moved off the bottom of the table thanks to Monday's 3-1 win at home to fellow strugglers Almeria.
"If Real fired me I wouldn't go to Malaga but to a big club in England or Italy," Mourinho said.
"Everyone has their way of behaving," he added. "I did not hear or read what he (Mourinho) said, nor will I reply.
"I know what it means to coach Real Madrid. Last year we tried our best, respecting the values of the institution."
"My office door is open for him and he is welcome to come and greet all the people who worked for him last year," the former Chelsea manager added.
As well as disrupting Real's bid to end Barca's two-year reign as Spanish champions it would also end Mourinho's nine-year unbeaten run in home league games.
