Wenger will oversee his 1,001st game as Arsenal manager on Tuesday night when Swansea arrive at the Emirates for head coach Monk's 10th match in charge.
And while Wenger is in the 18th year of his Arsenal reign, Monk is about to enter just an eighth week as Swans boss following Michael Laudrup's early-February exit.
But the former Swansea captain knows all about Wenger's influence on Arsenal, which was reinforced after spending time on Sunday with ex-Gunners stars Patrick Vieira and Sol Campbell.
"I have a lot of respect for him (Wenger). How could you not?" Monk said.
"I spent yesterday with Patrick Vieira and Sol Campbell doing my Pro Licence. I did my A Licence with them, too, and they had lots of good stories to tell about him and his time with Arsenal.
"They cannot speak highly enough of the guy, which says a lot, as they do not need to sugar-coat anything.
"They are honest enough and opinionated enough to tell you exactly what they think, and they see him as one of the best managers they worked with. He is a top, top manager - one of the best in the game."
At the head of Monk's agenda, though, will be a result for Swansea that would cause Wenger further strife following Saturday's 6-0 drubbing by Barclays Premier League leaders and title favourites Chelsea.
Monk was an unused substitute when Swansea won 2-0 thanks to a Michu double at The Emirates 15 months ago, and a repeat result would be heaven-sent for the Welsh club.
Last Saturday's 3-2 defeat against Everton kept them just four points above the relegation zone, with the Arsenal game being followed by a home clash against Norwich and then a trip to Hull.
"We can draw on experiences we have had before, like when we went to Arsenal last season and won," Monk added.
"It shows we can do it, and the players need to draw on that as motivation and for belief, but we are trying to get that belief into them for every game. The effort, desire and will to win are there, it is about slotting them all together.
"We went up there last season and were clinical and took our chances. That is what you have to do against the best teams in the league."
Monk has only experienced one win - a 3-0 Welsh derby success against Cardiff - since he took on the Swansea job.
"Defeats used to hurt as a player, and it is 10 times more as a manager," Monk said.
"But I have to stay confident, and I do. I believe in the boys, they believe in themselves, and they should do because we have a good bunch here who are working hard to get the results.
"It was never going to be easy, and anyone from the outside who thought it would be a magic wand was wrong.
"The thing is, you lose a manager generally because you are not doing well. That is the situation we were in, so it was not as if we were suddenly going to become a top, top team. It was always going to be tough and gruelling.
"It would have been great to come in and get four or five wins on the bounce and say 'we are safe now', but it was never going to be this way.
"On Saturday, the teams below us all lost, but you cannot rely on that.
"Every team plays each other in the next couple of weeks, and I think that is going to decide who is going to be in it right until the very end, so it is crucial we get points in the next three-four games to make sure we are not the ones having to fight until the bitter end."