Allardyce's Blackburn travel to Arsenal in the Premier League on Sunday after a week in which Wenger has celebrated a record 13 years in charge of the Gunners.
There have been few run-ins between the two managers over that period of time, with the Frenchman frequently criticising the physical approach of Allardyce's Bolton and Blackburn sides.
But while Allardyce admits there is no love lost between the pair, he hopes his opposite number has a certain level of appreciation for him and the success his style has reaped against Arsenal down the years.
Asked about their relationship, Allardyce said: "It's been interesting. I would hope that we have a mutual respect for one another, but other than that, it goes no farther.
"He's said about our aggressive nature in the way we've played against them, but it has always been within the rules and the laws of the game.
"Because we've adopted that side of it, he gets a little bit upset. But until football becomes a non-contact sport like basketball, then we will play within those rules.
"We always do that and it has brought us results against Arsenal - but that is why we have been criticised."
Although they have never entirely seen eye to eye, Allardyce was keen to pay tribute to Wenger's achievements since his arrival in north London in 1996.
"Anybody who can get into double figures as a manger these days is achieving a huge amount of success for their particular football club. There are few managers that can stay at a club that long.
"Arsene came from Japan and found his home at long last. He found he was allowed to do what he has probably always wanted to do, which was to run a football club his way.
"I think probably elsewhere, outside England, you are not allowed to do that, but in England, and particularly at Arsenal as the years have gone by, he's been allowed almost total control of the development of the football there.
"Both have benefited greatly from that so I'm not surprised that he's the longest-serving manager Arsenal have ever had."
Arsenal have already lost twice this season and although he has been impressed with their performances, Allardyce suggested that the sales of Kolo Toure and Emmanuel Adebayor could prove costly for the Gunners.
"They have been the same as usual - hugely talented, hugely entertaining, and there is another year's experience in his (Wenger's) players which has given them more guile to deal with the Premier League on a week-to-week basis and the Champions League," Allardyce said.
"I think the team has grown and got better. But it is a big risk and it will be determined at the end of the season how big a loss Toure and Adebayor were. That's Arsene's big challenge."
Blackburn go into the game off the back of a morale-boosting win over Aston Villa last weekend which took them out of the Premier League's bottom three.
Rovers currently have seven points but face a huge month ahead with fixtures against Chelsea, Manchester United and a derby with Burnley lying in wait, and Allardyce knows that his team will have to be at their absolute maximum if they are to make a positive start to October at the Emirates Stadium.
He said: "It's another very exciting game for us to go and play at the Emirates. It's a wonderful stadium but one at which we have to be extremely cautious about how we approach the game.
"We went there last year after beating Fulham and got completely dominated by an Arsenal side and I don't like seeing any of my teams and easily beat as we were.
"If we do go down, I want to see us go down with a big fight. If we don't, we get a result, and in the past I've never managed a victory but there have been a few draws over the years.
"We'll be planning to get at least that on Sunday, and if we get any more, it will be a massive bonus.
"There's no pressure on us really, nobody expects us to win, so we'll go and give it our best shot and hopefully turn out our best performance.
"We're going to need that at the very least, and even after that, you still might not beat them."
Arsenal 1/5, Draw 5/1, Blackburn 14/1