Wenger will leave Arsenal at the end of the season after nearly 22 years in charge, although the Frenchman has indicated he will seek another job in Europe.
Mourinho has said he regrets various rows with Wenger over the years ahead of the 68-year-old's last visit to Old Trafford with Arsenal on Sunday.
And the 55-year-old Portuguese suggested Wenger may be an example he looks to follow as he moves into the latter years of his managerial career.
"For sure, why not?" Mourinho told reporters when asked if he could match Wenger's longevity.
"This is a job where the more experience you have the better you are, you just have to keep up your motivational level. I believe that until a manager decides he has had enough and doesn't want any more you can still get better and better.
"Just look at the example of Mr Heynckes [Bayern Munich's 72-year-old coach Jupp]. He was retired, playing with his grandchildren or things like that, and suddenly he comes back to football and he is even better than what he was before.
"I think you can keep improving in this job, as long as you have some success. Sometimes people say enough is enough, but until that point arrives I think this is the kind of job where experience makes you better."
Wenger has yet to confirm his future plans but Mourinho expects the Arsenal manager to be in another job sooner rather than later, with a lucrative switch to the Chinese Super League among his reported options.
"I don't think Arsene is going to end his coaching career," Mourinho said. "As far as I know he is only finishing at Arsenal.
"I am sure Manchester United fans will remember all the years when Arsenal were their biggest rivals, and I am going to remember Arsene as a big opponent, the manager of the Invincibles. That was my first year in this country.
"When I arrived in 2004 Arsenal had just won the title without being beaten. I would say the Invincibles made me a better coach and that is the way I will remember Arsene, although I should say he is not yet dead. I doubt if he is finished with football."
While Mourinho hopes he has a long time to go as a manager, an extended period at United – following Wenger's example at Arsenal and Alex Ferguson at Old Trafford – may not be possible due to outside influences
"You would not allow it – media, social media, the pundit industry – I think it is too much pressure, not just for the manager but also for the club," added Mourinho, who signed a new long-term deal this year.
"I don't know how long I will be at United but I don't want to be anywhere else. To be honest, at all my other clubs I had the feeling of already thinking about what to do next. I had things to do. I had to go to Italy, for sure. I had to go to Spain, for sure.
"They were things I really wanted to do but at the moment there isn't anything I have waiting around the corner. I don't want to do anything different from what I am doing now."