Mourinho was speaking at his unveiling as United manager and although he mentions no names it seems rather apparent who he is referring to.
The animosity between the two extends back many years and is best encapsulated during 2014 when Mourinho called the Frenchman a "specialist in failure" and the two were also embroiled in a touchline shoving match whilst the Portuguese was still at the helm of Chelsea.
During his time at the Blues Mourinho oversaw the successful capture of three Premier League titles, whilst Wenger last lifted that particular trophy in 2004.
"Some managers- the last time they won a title was 10 years ago. Some of them- never. The last time I won a title was a year ago. So if I have a lot to prove, imagine the others," said Mourinho.
"The reality is it was never important for me. I play against myself. I have to prove not to the others but to myself, that's my nature. I would never be able to work without success.
"I have to always find the reasons why I have as many questions towards myself and the people working with me, that's my nature. I could approach this job in a defensive point of view by saying 'the last three years the best we did was fourth and an FA Cup.'