The Chelsea boss and the Frenchman endured a difficult relationship during the Mourinho's first stint at Stamford Bridge, when he infamously called his Gunners counterpart "a voyeur" for commenting on his rivals.
However, Mourinho told how a series of chance meetings at several football tournaments following his 2007 Chelsea departure led the two men to form an unlikely friendship.
"I started meeting him in UEFA, at the Euros (European Championships), the World Cup, we had dinner and so on," the Portuguese said in several newspapers today.
"And when you are not in the same league and when you are not playing against each other, it is easier 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 my respect always. (In) football sometimes even if you are friends and respect each other, 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 on one single problem between us."
Mourinho also claimed he never doubted the intentions of Chelsea owner Roman Abramovich.
The pair parted ways by mutual consent in September 2007, with Mourinho leaving the club as its most successful manager with six trophies in three years.
However, the self-titled 'Special One' returned to the Blues this summer after spells at Inter Milan and Real Madrid, and hailed the Russian's foresight.
"There was always the question, 'When is he going to sell it?' 'Is he in love with the club?' 'Is he in love with football?' 'Is he doing this for the right reasons?"' Mourinho said.
"Peter Kenyon (then chief executive) and I were worried about just creating the right conditions and having a good base. Roman was always going for more, always going for the future. He said, 'If we can build 15 pitches here, why build only four?'
"We said: 'Because four is what we need now - two for the first team, one for the reserves and one for the youth'. He said: 'No, no, if we can build 14 or 15, then do it for the future, for the kids. The thing is not just to have the reserves and the first team here, it's to have all the teams here. Why train at Brentford if we can have everybody here? So the academy has the same conditions as the first team'."