Mourinho and Guardiola had a volatile relationship when the Portuguese was in charge of Real Madrid and the Spaniard was at the helm at Barcelona during the 2010-11 and 2011-12 seasons.
But because of the competitive nature of the Premier League, new United boss Jose believes it could damage his team’s title hopes and vice-versa for Pep at City.
The Special One says: “My experience does not allow me to be naive. What I mean by that is that I was with Pep for two years in a championship where the champion was either him or me, Real Madrid or Barcelona.
“In a situation like that individual battles make sense because they can have an influence.
“If, in the Premier League, I focus on him at Manchester City and he on me at Manchester United, another team will win the title.”
The new United and City managers face an early confrontation when their sides meet in a friendly in Beijing on July 25.
Last season City were ahead on goal difference but pipping United to fourth position meant they took the final Champions League qualifying place, leaving the Old Trafford club to settle for a spot in the Europa League.
Mourinho said he could not afford to focus on Guardiola if he wanted to bring the league title back to United for the first time since 2013.
“Look at the Bundesliga ... in the last five years the same team won the title four times and in France the same team won the last four,” he said.
“In Spain Atletico won once and Barcelona the other three. In England there have been four different champions in the last four years.
“That says a lot about the competitiveness. The fact it has the biggest television rights and that the television revenues are distributed in the way that they are, allows the league to grow...”