Madrid-based sports daily AS claims that City are willing to pay the €4 million ($5.2m) release clause in Pellegrini's contract to take him from the financially troubled Spanish club.
The Chilean, who led Malaga the quarter-finals of the Champions League in their first ever appearance in the competition this season, is thought to have been targeted by former Barcelona sporting director and now director of football at City, Txiki Begiristain.
Begiristain has been impressed with his success in that competition compared with current manager Roberto Mancini's failure to get City beyond the group stages in the past two seasons.
Begiristain met with Pellegrini's agent Jesus Martinez last month in Madrid and AS also claim that, should Pellegrini move to Manchester, that could clear a way for talented Malaga playmaker Isco to become City's latest big-money signing come the end of the season.
Mancini, speaking on the eve of Manchester City's FA Cup final loss against Wigan, was philosophical about his own position despite leading them to a first major trophy in 35 years when they won the 2011 FA Cup.
"I won seven trophies at Inter in four years and they sacked me after four years," said the 48-year-old at his pre-match press conference.
"This is football. I know football enough to understand this situation."
The Italian was also responsible for overseeing last term's Premier League success — the first time City had been crowned champions of England in 44 years.