But the City manager claims he could not work properly if he let such rumours affect him.
Bayern Munich's much-coveted former Barcelona boss has been a reported target of City for several years, dating back even before Pellegrini arrived at the Etihad Stadium in 2013.
The stories have resurfaced in recent days because Guardiola has suggested he will make an announcement about his future in the next week.
But Pellegrini, who was displaced by Jose Mourinho at Real Madrid in 2010, said: "We don't know what Pep will do next season. There are rumours, speculation about what he wants to do.
"I think Pep is one of the best coaches in the world so if he doesn't continue at Bayern, maybe a lot of teams can try to have him manage their team.
"In my case, I don't have any pressure about that. Maybe there are a lot of rumours - not only this season but going back to the other seasons - but the only pressure I feel is the pressure I put on myself to win.
"When you have experience and manage so many big clubs you know with every result that is not the result the club wants, the media will start with different rumours about different things, but if you are worried about that it's impossible to work in a big team."
Pellegrini guided City to Premier League title success and the Capital One Cup in his first season in charge. Their defence of their league title last season was poor but they still finished second and are the favourites to take the crown this term.
Such facts weigh heavily in Pellegrini's favour and, given the recurring speculation over his future, he could perhaps argue that his achievements are under-appreciated.
But he insists he feels no such thing and is not motivated by any desire to change people's perceptions of him.
The 62-year-old said: "I don't think like that. For me it's not important. For me the only important thing is to see what I did in my career.
"If I finish this season winning the Premier League, and in three years winning two Premier Leagues with one runner-up, that is very important. If something is not considered important I can't be arguing with different media. I'm very happy about my career and my work.
"I would not be happy if I don't win silverware this season but all the other things I cannot be thinking about. Everyone can have their opinions.
"You're going to have good performances, bad performances, you'll be criticised, receive praise - different things - but you can't be too concerned about those things."
Reclaiming the title and perhaps winning other silverware this season would make any decision to remove Pellegrini next northern summer, even if Guardiola was available, seem particularly harsh.
But the Chilean, who is contracted to 2017, said: "I cannot talk about what other people want to manage the club. Every owner has the right to see what is the best future for their club.
"It's not my problem because I don't think for them. My thinking is to try to win and continue in a job where I am happy. After that it's not my decision."