Mourinho and Guardiola were rivals in the Primera Division while in charge of Real Madrid and Barcelona respectively and will face off once more in Manchester next season.
United named Mourinho as their manager last week while Guardiola was appointed by City in February to replace Manuel Pellegrini.
However Mourinho, who pipped Guardiola's Barcelona to the Primera Division title in 2012 but finished runners-up to the Catalan club twice while in Madrid, has no intention of focussing on personal duels.
Mourinho, quoted in several national newspapers, said: "(What has happened in the past) does not allow me to be innocent
For two years Pep and I were in a league where the champion would be either me or him, Real Madrid or Barcelona."
Speaking at Lisbon University's Faculty of Human Kinetics, he added: "In a situation like this, individual fights make sense because they can influence things.
"[But] in the Premier League, if I focus on him and Manchester City, and he on me and Manchester United, someone else is going to win the league."
Leicester were the shock winners of the latest Premier League title and Mourinho expects the competition to be as fierce as ever next term.
He said: "The level of the Premier League is going to get better with the players and coaches who will come.
"Four champions in four years (Leicester, Chelsea, City and United) shows how competitive it is, and also says a lot about the television rights and its distribution, which will allow the growth of the league and all its teams.
"It is different to other leagues where the sharks will always be sharks."
Source : PA
Source: PA