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.
Under Pellegrini, a softly-spoken, elegant man with a professorial bearing, in contrast to the brash and flamboyant Mourinho, Real amassed a club record La Liga points total of 96.
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.
Pellegrini, who joined Real after a successful stint at Villarreal, was given the Malaga job after the Andalusian club were taken over by a member of the Qatari royal family.
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.
Real, meanwhile, have slipped seven points behind leaders Barca with 25 matches played this term.
At the same stage last season, they topped the table on goal difference from their great rivals with 62 points, one more than their current total.
The combative Portuguese Mourinho did his best to rile his predecessor at a news conference on Wednesday but Pellegrini refused to rise to the bait at a later briefing.
"If Real fired me I wouldn't go to Malaga but to a big club in England or Italy," Mourinho said.
Pellegrini responded by saying it was an honour to coach Malaga, especially as he had been given the task of saving the club from relegation.
"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."
Mourinho acknowledged that Real put together a good league campaign last season and said he hoped Pellegrini was well received by the fans on Thursday.
"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.
If Pellegrini wanted to make a point to his former employers and his replacement, what better way than engineering a win at the Bernabeu.
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.
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