The pair have history dating back to their time in Spain, where the Portuguese replaced Pellegrini at Real Madrid after finishing second to Barcelona with a record number of points.
Mourinho announced "Second place is just the first loser. If Madrid were to fire me, I wouldn't go to Malaga. I'd go to a top-level team in Italy or England."
But Pellegrini is not interested in revisiting past disagreements as they come face-to-face again in England for the first time on Sunday.
"I never get involved in the moment and I will not get involved now," he said.
"I don't know him. He worked in Spain, I worked in another club.
"We played Real Madrid against Malaga. Nothing more, I don't have any complaint about him."
Asked whether they were very different characters Pellegrini added: "Maybe (we have) a different way of thinking about life."
Sunday's clash at Stamford Bridge sees the team second in the table face-off against the team in fourth spot and Pellegrini is looking forward to the game.
"Of course it is an important moment, (it is) always important playing against a team that has a lot of chance to win the Premier League," added the Chilean.
"I repeat the same thing I said when we played against Manchester United, it is a match of six points.
"They play at home, this is our third (successive) game playing away. We hope we can continue winning the same as in both (previous) games.
"This is the ninth (league) game. We have a lot of games in the future.
"It is not the important game of the year. It is an important game but it will not decide nothing."
Chelsea v Manchester City is live on Sky Sports 1 HD from 3:30pm on Sunday.