The Chilean is said to have taken the decision following a handful of errors by the the England number one so far this term.
As a result, speculation has claimed that Pellegrini may delve into the transfer market for a new shot-stopper, either during the January window or next summer.
So, with that in mind, Sports Mole has picked out five keepers that could potentially replace 26-year-old Hart.
There was once a time when it was unthinkable that Casillas would not be between the posts for Real Madrid. The 32-year-old established himself within the Los Blancos starting lineup in 2000 and having taken over the captaincy from Raul, it appeared that he would end his career at the Bernabeu. Jose Mourinho dropped him in favour of Diego Lopez last season, though, and new Madrid coach Carlo Ancelotti has stuck with that theme. Consequently, it is believed that one-club man Casillas would consider a move away to keep his place in the Spanish national side. He would bring to City a wealth of experience from successful campaigns in the Champions League, European Championships and World Cup, while 32 is by no means old for a keeper.
Breathing down Casillas's neck in terms of the national team is Barcelona stopper Valdes. Unlike Casillas, the 31-year-old is still the first choice with his club. However, his contract at the Camp Nou is due to expire next summer and Valdes has insisted that he has no intention of signing an extension to those terms. But why leave the Catalan outfit? It's thought that having joined the La Liga champions in 1995, Valdes is keen to take on a new challenge. Although money is no real object to City and their wealthy owners, there can't be many managers out there that would turn down a player of Valdes's quality for free. Having developed under the guidance of Pep Guardiola, Valdes is arguably the most gifted keeper with the ball at his feet.
As a youngster at Portsmouth, Begovic was loaned out on five occasions to gain some match experience. He was sold to Stoke City in 2010 and since then has gone on to prove that Pompey's loss is Stoke's gain. Having ousted the experienced Thomas Sorensen to claim the number one jersey, Begovic's performances have resulted in him being linked with a host of clubs, including Manchester United, Barcelona and even City. There are a number of very good shot-stoppers in the Premier League at this present moment in time, but the Bosnian international is also dominant inside his own area.
If Pellegrini is looking to recruit someone that he can trust, look no further than Caballero. The now City boss signed the 32-year-old during his stint at Malaga and he kept goal as unfancied Los Boquerones qualified for the Champions League in 2012. What's more, he then excelled as the Spanish outfit reached the quarter-finals of the competition before they were knocked out in controversial circumstances by eventual finalists Borussia Dortmund. The 32-year-old showed his credentials during a recent match against Real Madrid, where he made 13 saves.
The 25-year-old is vying for Hart's place in the England team, so perhaps he could really rub salt into the wound by replacing him at club level as well. Forster has really rose to prominence since his switch to Scottish champions Celtic from Newcastle United in 2010. Some will argue that the standard of football North of the border is not the greatest, so a switch to the Premier League would represent a big step up. However, Forster has proved himself in the Champions League against a host of clubs, including Lionel Messi and his Barcelona teammates.