The pair go head-to-head at Old Trafford on Monday where Moyes will be looking to claim his first victory over the charismatic Portuguese coach, having failed to beat Mourinho during his first stint at Chelsea, whilst he was still at Everton.
But their respective status' at the helm of two of England's biggest clubs has not put the pair in conflict.
Mourinho has spoken highly of Moyes and the United boss is glad to have an old foe back.
"He was enjoyed by the media. Chelsea supporters obviously enjoyed him," said Moyes.
"From that point of view I would say yes (the Premier League has missed him)."
Moyes wrote to Mourinho following his dismissal by Chelsea to wish him good luck for the future.
And the United boss was not impressed during the summer when it appeared a feud was being built up between them.
"I have not seen him for a long time," said Moyes.
"Our paths have not crossed - probably because I was never in the Champions League, we have not had any reason to meet.
"I am looking forward to seeing him again though.
"He is probably the best of the young, modern coaches in the world. "He is the one who has had the most success. He deserves all the plaudits he gets."
Moyes does not view Mourinho's job as being less pressurised than his own, even though their respective CVs boast a hugely differing list of honours.
After all, he has been chosen on merit by Sir Alex Ferguson after 11 excellent years working on a limited budget at Everton.
So far, Moyes has handled the situation well.
He has carried out the tricky balancing act of paying tribute to Ferguson's vast achievements without allowing them to overshadow him.
And for all the firsts he is currently experiencing, Moyes keeps stressing he is merely continuing a job he spent so long in, at both Preston and Everton.
But he accepts Monday will be a little bit special.
"There has been a lot of things I have been looking forward to; taking the team on tour, leading them out at Wembley. But to do it at Old Trafford for the first game against Chelsea is a thrill for me, it really is," he said.
"It has come quickly.
"I knew what it was like. This is a monster in terms of the size of the club. Getting to know everybody is not that easy.
"It will take me a long time to get to know how it works.
"The bit I have enjoyed has been getting the know the players. They have made my job very easy.
"They have been excellent with their level of professionalism and the way they have gone about their work."