Allardyce has enjoyed some success against Arsenal over the years with Bolton and Blackburn, and they secured a 2-1 win over the Gunners at Ewood Park in the teams' penultimate game of last season.
Allardyce and Wenger have often criticised one another in the press as a result of their differing philosophies on the game and, on the subject of sharing a drink after the game, Allardyce said: "He's never been the type of man to do that and neither have most foreign coaches that have been here. Rafa Benitez was the same and Carlo Ancelotti never came into my office last year.
"British coaches see it as an unwritten rule that no matter what they pop in and see the manager after the game. It has never been the case with Arsene but that does not particularly worry me. What worries me is making sure that we must not let them beat us.
"We must not let them use their skills and that is a big concern to us because they are one of the top teams in the country. For many years we have pitted our wits against each other and when you've had some success over that time then you obviously remember how you did it."
Meanwhile, Allardyce confirmed Blackburn are edging closer to a deal for Benjani, who is available on a free transfer after leaving Manchester City.
"We are trying to sign him on a contract because of his wealth of experience," he said. "He has trained with us a few days. He has shown us that we think he will be okay to play for us in the Premier League, so we are trying to sort something out."