Mourinho succeeded the Chilean at Real Madrid before returning to the Premier League with Chelsea, while Pellegrini's career path took him from the Bernabeu to Malaga and on to Manchester City this summer.
Reports of bad blood between the pair stem from a comment made by Mourinho on his arrival at Real, when he said: "If they get rid of me I won't be going to coach Malaga. I will go to a big club in the Premier League."
Mourinho went on to win six of his eight meetings with Pellegrini's Malaga during his time in Spain, drawing another and losing just once.
Sunday's Stamford Bridge contest will be their first in England, and Pellegrini was keen to concentrate on the football at his pre-match press conference.
He said: "It is a tough game for Manchester City. We are one point behind Chelsea. We must play a very good match if we want to win.
"I don't know him (Mourinho). We worked in Spain, I worked at another club. I don't have any complaint about him. Maybe we have a different way of thinking about this life. I never get involved and I will not get involved now.
"It is always an important game when you play someone who has a chance to win the Premier League.
"I repeat what I said when we played Manchester United, it is a game of six points."
Chelsea v Manchester City is live on Sky Sports 1 HD from 3:30pm on Sunday.