City have been heavily linked with Pellegrini in recent weeks and speculation has intensified since last year's Barclays Premier League-winning boss Roberto Mancini was sacked last week.
Mancini paid the price for failing to meet the club's high expectations after his side lost their title and slumped out of the Champions League prematurely.
The Italian remained a firm favourite with fans having also ended a 35-year trophy drought by winning the FA Cup in 2011 but the club feel it is time to move on.
Chief executive Ferran Soriano was quizzed about the matter by a US television reporter as the club formally announced the launch of their new Major League Soccer team.
When asked what Mancini did wrong, Soriano told CNN: "He did very good things for the club.
"He stayed there for three years, which is a lot of time. He brought the club to a winning club.
"Now we are just looking for the next step, the next cycle.
"We have a fantastic squad. We want to play better football and we want to continue winning.
"It is not that Mancini did anything wrong. We are just in another cycle, in another era."
In their statement that announced Mancini's departure, City referred to the need to develop a "holistic approach" to all aspects of football at the club.
It had previously been rumoured City wanted to introduce a fluid 4-3-3 style of play to all their sides, from junior level up to first team.
When asked about that matter, Soriano said: "We are looking to play very good football, very beautiful football.
"When we are playing good football, then we will win.
"So it is not only about winning, it is developing football that is attractive and it will be played by our main teams, our first team in Manchester, our young teams in Manchester and also our teams in New York.
"We want to share the same football concepts across all our teams."
Pellegrini is the odds-on favourite to take over at the Etihad Stadium and it is now clear that he will be available.
The 59-year-old, who guided Malaga to the Champions League quarter-finals this year, had indicated a desire to leave and the Spanish club have now confirmed he will depart at the end of their season.
Pellegrini told the club's website: "Malaga has a story without Manuel Pellegrini, and (is) also going to have a future without Manuel Pellegrini.
"(I have) an eternal gratitude to the club's owners, who trusted me blindly."
The club also confirmed what Pellegrini had been quoted as saying at a civic function earlier in the day, that the coach was leaving for "sporting reasons".
Pellegrini denied earlier this month that he had an agreement in place with City.
"My coaching staff and I have separated from Malaga but our union with this city will be eternal," he said.
"We had a time with the club that was very rewarding. Everyone has the right to move on.
"Sunday will be my last match at La Rosaleda and will be very exciting for me.
"I'm not leaving due to the matter of money but looking for a project that allows me to develop my profession conveniently."
Pellegrini has been at Malaga since November 2010 after previous spells with Villarreal and Real Madrid.
His team have two games of their season remaining, against Deportivo La Coruna and Barcelona.