Pellegrini is expected to replace Roberto Mancini, who was dismissed as City's manager a year to the day after guiding the club to its first Premier League title in 44 years.
City's slow progress in Europe was a major factor behind Mancini's firing, with the club failing to emerge from the Champions League group stage for the second consecutive season.
Malaga confirmed on Wednesday evening that Pellegrini will leave the Spanish club at the end of the season, while the 59-year-old is City's first-choice replacement for Mancini.
"It's tough to talk about possibilities obviously," Hart told Goal. "We had successful times under Roberto but the club's made the decision to move forward and we need to react as players. Whoever comes in, we'll give them everything we've got."
Hart was among those in City's squad last season who were publicly criticized for his performances by Mancini but the England international is adamant that the club is not in need of wholesale changes.
"We need to improve on next year and that's an exciting challenge," said Hart. "There's nothing massive, just little tweaks here and there. Finishing the job - we didn't win enough games - we won possession, dominated games, but didn't win them. That's what we need to improve on."
Hart added that "there's a lot of work to be done behind the scenes" as City looks to recover from last season's disappointing run, which saw the club finish second in the league behind rival Manchester United.
"That's why we've got such great people in charge - strong characters, strong businessmen - hopefully they're going to make the right decisions and we're going to react as players, which I'm sure we will, and we need move forward," Hart said.
"Everything's in the past now, that's the beauty of football - it's constantly changing - and we have another chance next year."