The pair have found themselves involved in a war of words during their spells in charge of the London sides, with Mourinho recently claiming that Arsenal’s decade-long wait to win the Premier League title was “boring”.
However, Mourinho expects that Arsenal will offer a stern challenge to his side next season.
“I believe they [Arsenal] have a top manager, I’m not making fun here,” the Portuguese told BT Sport.
“They will be even harder to beat next season.”
Mourinho guided Chelsea to their fourth Premier League crown last term.