Speaking ahead of Arsenal's visit to Stamford Bridge on Saturday, when their French manager marks his 1,000th game in charge, Mourinho said he would like to emulate Wenger's longevity.
"I admire him and I admire Arsenal," the Portuguese told reporters.
Mourinho being Mourinho, he could not resist a sting in the tail to the praise for a manager whose side have not won a trophy since 2005.
"It is not possible to have 1,000 matches unless the club is also a fantastic club in the way they support their manager, especially in the bad moments and especially when the bad moments were quite a lot," he said.
"The tribute is to say that I believe any one of us (managers) would love to have the same privilege with our clubs. Could I stay for 1,000 games? I would like to, but it's very difficult.
"It's even more difficult in modern football. If I can reach 500 with Chelsea it would be fantastic."
Mourinho is in his second spell at Chelsea, returning last June after a first stint that began in 2004 and ended in 2007 following a fallout with billionaire Russian owner Roman Abramovich.
In his first stint, the Portuguese won the 2005 and 2006 Premier League titles, the FA Cup in 2007 and the League Cup twice.
Chelsea currently lead the league with a four point advantage over Arsenal and Wenger needs no extra motivation to beat them at Stamford Bridge after dismissing Mourinho's comments last month as "silly" and "disrespectful".
(Reporting by Alan Baldwin, editing by Martyn Herman)