The two have clashed in the past, particularly during the Portuguese's first spell at Stamford Bridge, when he famously called the Gunners coach a "voyeur".
However, Mourinho insists that he now gets on well with the Frenchman and that their relationship has progressed during his time away from the England.
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"I think I met him a few times, we had dinner and so on. When you are not in the same league and when you are not playing against each other, it is easier to get to know people, it is easier to go deeper. It is easy to speak about football. He's a very nice guy.
"I respect him a lot and I will show it always," Mourinho added of his intent to be less antagonistic this season.
"In football, things like this happen. Sometimes, even if you are friends and respect each other, sometimes you say something the other doesn't like and you react but, at the end of the day, I respect him a lot and I have the feeling that he is the same in relation to me.
"I wouldn't bet for one single problem between us."