The 36-year-old midfielder was released by the Blues earlier this summer after 13 years at Stamford Bridge, in which time he secured legendary status at the club and leapt to the top of their scoring charts.
He is now technically a New York City FC player after penning a contract with the American club, but they will not enter the MLS until next year which left him free to join another side in the meantime.
With NYCFC part owned by Man City, the veteran star elected to sign a short-term loan deal with them to prolong his Premier League career and maintain his fitness.
This has irked many Chelsea fans, who are upset at the player’s decision to sign for a direct title rival due to his close ties with the London club.
However Pellegrini cannot comprehend the criticism as Jose Mourinho’s side elected to release Lampard:
“I don’t understand the reaction of Chelsea fans who say he is a traitor,” he is quoted by The Mirror.
“The problem was not that Frank Lampard did not want to sign another contract with Chelsea – Chelsea didn’t want him any more.
“He is a competitive player, he will be important for our team and we didn’t spend any money on him, so the rules of financial fair play don’t have any relation with Lampard.”