Allardyce has long had a fractious relationship with Wenger, and the Blackburn manager has revealed that he has found him difficult from their first meeting over a decade ago.
"I first met Arsene Wenger in 1999 when I was manager of Notts County and we sold Jermaine Pennant to Arsenal for a record £2million," he said in his News of the World column. "I was really looking forward to meeting him but all I got was a handshake. No more.
"We have crossed swords many more times in the years since but I gave up inviting him for a glass of wine after games long ago because I know he won't come.
"The truth is that nobody really knows Arsene Wenger. There certainly aren't too many people who actually get close to him. Sir Alex Ferguson and some of the foreign coaches like Avram Grant always pop in for a drink so I don't think it's a problem with my wine!
"If that's Arsene's way, though, then I respect that. Maybe he doesn't like me. Maybe he is keen to get on the coach or the plane after fulfilling 45 minutes of post-match media duties."
Allardyce repeated his claim that Wenger is using the media to influence referees in the column, but added: "None of all this affects my view of Wenger.
"I have total respect for the way he changed his philosophy in recent years when the £400 million move to the Emirates Stadium reduced his spending power in the transfer market.
"He hasn't won trophies yet with his current crop but he has stuck to his guns by insisting that nothing will prevent the development of his young players. Arsenal play some wonderful football but what makes the Premier League interesting is the difference in styles between teams."
Allardyce says, though, that he believes he is on an equal footing with Wenger when it comes to management.
"When I say what I think there are people who say "Oh, it's only antiquated Sam Allardyce", and all kinds of b******* like that," he said. "There is a problem with perception.
"Arsene is seen as a sophisticated Frenchman while I'm just a rugged English centre-half from the Midlands with an accent to match, but is Arsene more advanced than me in terms of coaching? Not a chance.
"Does he use live fitness data on his players during games? Does he study sports psychology every day? Does he use sports science to the extent that I do? I doubt it."
Allardyce also revealed he was disappointed to see Rafael Benitez leave Liverpool this summer.
"I am gutted that Rafa Benitez has gone. He hated me and I used to love winding him up. For years he came to Bolton and never got a result and used to accuse us of cheating."