Pellegrini's City side are still vying for silverware in four competitions this season and are firmly in the race for the Premier League title after thrashing Crystal Palace 4-0 at the weekend.
Guardiola took the unusual step of announcing to the world his intention to manage in the Premier League next season midway through Bayern's Bundesliga campaign, as reported by Sky Sports.
But City's Chilean boss has been seemingly unfazed by speculation that his replacement has already been lined up.
David Moyes is a man who knows all about the impact intense speculation over your job can have on performances after his dismal spell as boss of City's bitter rivals United.
'I think he's doing well'
And he has told BBC's Match of the Day he admires the way Pellegrini and his team are dealing with the situation.
"He's handling it fantastically well," Moyes told MOTD.
"Every time he's put in front of the press he answers very clearly, concise with what he says and I think overall the team is dealing with it quite well.
"They're still in four competitions so I think that he's doing well but I do think that it's never nice for a manager when you think that someone's coming to take your job.
"I'm sure from his point of view he'll be saying 'well if I can win all of these competitions then it's a big decision not to keep me'."
Anxiety and money fuels speculation
Moyes is right, talk over Pellegrini's future seems rather harsh.
But that comes from the huge expectations that City should be more dominant domestically thanks to their vast riches and expensively assembled squad.
However it must be remembered they have suffered with injuries to key players like captain Vincent Kompany and strike star Sergio Aguero all season long and Pellegrini often struggles to field the same team in consecutive games.
And perhaps most significantly City's anxiety to get Guardiola signed up comes as their major rivals at Old Trafford and Chelsea could well be in the hunt for a new boss come the summer.