Pellegrini acknowledges that the pair have had their differences but does not want that to detract from Sunday's clash between the two Barclays Premier League title heavyweights at the Etihad Stadium.
The two managers have a rivalry dating back to when Mourinho succeeded Pellegrini as Real Madrid boss in 2010 and made unflattering comments about his predecessor
They did not shake hands after their first meeting in England in October 2013, when Mourinho's Chelsea snatched a late Fernando Torres winner at Stamford Bridge and the Portuguese celebrated extravagantly.
Mourinho was involved in another handshake incident a fortnight ago when he did not acknowledge Arsene Wenger after Community Shield defeat to Arsenal.
But Pellegrini said: "I said the first day I arrived here I have my differences with him but..
I always shake hands with him."
Pellegrini feels it is important to get a good result this weekend to send out a strong message for the season ahead, even if it is too early to talk about the encounter in terms of its title significance.
The Chilean, who has beaten Mourinho just twice in 13 attempts in England and Spain, said: "We are not thinking about the title in the second game but we are thinking about trying to win our points at home, especially as we are playing against the champions and one of the teams that has a lot of chances to win the title.
"It is the same as Manchester United, Arsenal, Liverpool, Tottenham - all the big teams."
Chelsea began the season as strong title favourites but City's convincing win at West Brom has provided a strong reminder of the credentials of Pellegrini's men
Chelsea have also had a troubled week with their frustrating draw against Swansea, which saw goalkeeper Thibaut Courtois sent off, followed by a row over their medical staff's treatment of Eden Hazard during the game.
Pellegrini did not want to be drawn into commenting on that matter and claimed it would make little difference to players' preparations for the game anyway.
He said at a press conference: "I cannot give you an opinion about what happens at another club.
"The players will be more interested in the game
They will be trying to win
I think it will be just a game involving football things and not other things."
Pellegrini would not comment on continuing reports claiming City have lodged a £47million bid with Wolfsburg for Kevin de Bruyne or rumours linking the club with apparent Manchester United target Pedro of Barcelona.
He said: "I don't talk about rumours
We have a good squad at this moment but if we can improve it in a couple of positions it is better."
Sunday's game will be the first at the Etihad Stadium since the opening of a new 6,000-seat tier on the South Stand and the addition of 1,500 extra pitchside seats, with the full capacity now 55,097.
Source : PA
Source: PA