The two all-star managers had a memorable rivalry during their respective stints with Barcelona and Real Madrid.
Guardiola insists the new season is about more than just his battle against Mourinho but admits their conflict spurs him on to get better and better.
He said at his first official press conference as City boss: "We're both here, Jose and I. He wants to win, I want to win. We know each other pretty well.
"Competing against managers like that take you to the next level, they push you to achieve things.
It's not about him or me. It's doesn't matter about the team, it's so difficult to win here.
"We played many times against each other and the big coaches like Jose, they helped me reach another level as a coach."
City have already completed deals for Ilkay Gundogan, Nolito, Oleksandr Zinchenko and Aaron Mooy this summer.
Guardiola gave little away when asked who he would be targeting in the rest of the transfer window.
He added: "This is not the right place to explain about the new players out of respect to the players and the other clubs.
"You will discover in time what is our target and what we want for the next season. We will try and move the squad a bit."
Guardiola was also asked if he had received any other offers to come to England before landing his role at the Etihad.
He said: "Seriously it was just one.
"I will be grateful to this club for the opportunity to come to this club, this country.
"Manchester City gave me this opportunity, this challenge and I will do my best to achieve."
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