Arsenal's most recent silverware came in the 2005 FA Cup; in his 500th, they lost to Mourinho's Chelsea, who successfully defended their Premier League title in 2006.
"I admire him and I admire Arsenal, because it's not possible to have 1,000 matches unless the club is also a fantastic club in the way they support the manager, especially in the bad moments and especially when the bad moments were quite a lot," Mourinho said.
The pair endured a frosty relationship during Mourinho's first spell and a truce proved temporary when the Portuguese felt so riled by Wenger last month that he re-engaged the hostility.
Mourinho described Wenger as a "specialist in failure" after the Frenchman commented that anyone ruling themselves out of the title race was doing so out of a fear of falling short.
Mourinho's reaction was perhaps due to Arsenal, along with Liverpool and Manchester City, being rivals as the Blues chase just a second Premier League title since 2006 - Carlo Ancelotti led Chelsea to the 2010 championship - this season.
The Chelsea manager on Friday refused to apologise for the "failure" barb, after which he felt he was unfairly portrayed as the villain, and stopped short of joining those lauding Wenger's career.
"The tribute is to say that I believe that any one of us would love to have the same privilege (of getting to 1,000 games) with our clubs," Mourinho said.
Mourinho's career has seen him enjoy short and successful spells at Porto, Chelsea, Inter Milan and Real Madrid and now back at Stamford Bridge.
He respects Wenger's longevity, particularly in the modern game, and hopes to emulate it, at least in part, with the Blues.
"It was always difficult, but in modern football it is even more difficult," he added.
"If I accumulate my first three-and-a-half years with Chelsea and this one, I have a few.
"And let's see if I can reach, not 1,000, but I would say, 500 (matches)
It would be fantastic."
The landmark occasion comes with Wenger chasing a first victory in 10 contests with Mourinho, who has not been beaten in 75 Premier League matches at Stamford Bridge.
Mourinho insisted his personal record against Wenger was incidental as matches pit team against team, not manager against manager.
"It doesn't matter," he said
"It's not against him
It's Chelsea against Arsenal.
"I didn't even play Arsenal with Inter Milan or with Real Madrid or with Porto, I just played with Chelsea.
"It's Chelsea-Arsenal, Arsenal-Chelsea, it's not me against him.
"Records don't play any role
A match is a match
It's not coach against coach, it's team against team."
Chelsea, who beat Galatasaray to advance to the Champions League quarter-finals in midweek, will be bidding to respond to last Saturday's controversial loss to Aston Villa, when Mourinho, Ramires and Willian were sent off.
Mourinho will contest his Football Association improper conduct charge, while Ramires is banned for three matches and Willian one, with both missing the Gunners visit.
After the Villa Park loss Mourinho called for the Premier League not to assign referee Chris Foy to Chelsea matches in future - something which will not happen as it would set a dangerous precedent - and it is clear the manner of the defeat still rankles.
Mourinho added: "Last Saturday put us in a position where probably we wouldn't be now
Probably we'd be with more points than we have now."
Also absent on Saturday is former Arsenal left-back Ashley Cole (knee), but Nemanja Matic and Mohammed Salah are available after being ineligible in Europe in midweek.
Chelsea were drawn with Paris St Germain in the Champions League last eight, something which will give Mourinho reason to once again question UEFA's Financial Fair Play regulations.
The Blues say they are trying to live within their means while others continue to spend astronomical sums.
Speaking before his side were drawn to play a PSG featuring Zlatan Ibrahimovic and Edinson Cavani, Mourinho suggested the other six teams would be keen to play his side or Manchester United, once again deploying the underdog card.
"Maybe all of them want us, because Chelsea's maybe the outsider of the group," Mourinho said.
"Maybe us and Man United, because they're not having a great season."
Source : PA
Source: PA