Allardyce's Crystal Palace welcome the Gunners to Selhurst Park on Monday amid growing tension between the Arsenal boss and supporters following another unsuccessful Premier League title challenge.
A section of Arsenal fans staged another protest in their 3-0 victory over West Ham on Wednesday as they stayed away from their Emirates Stadium seats until the 13th minute - 13 signifying the number of years since they last won the league.
Former England boss Allardyce is not surprised by the recent climate at Arsenal, where Wenger is due to reach the end of his contract this summer.
Asked if Wenger should be making his plans for next season known, Allardyce said: "Not really, that's a conversation that the club has, not Arsene himself. The whole club decides if you're going to make an announcement or not, not just the manager."
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On the protests against the Frenchman, Allardyce said: "It's the norm...today. It's what you have to accept across the board as a manager, that there will be criticism thrown your way at some stage if people think you're not achieving what you should achieve.
"We've all had it but we're tough enough to deal with it. He's been an outstanding manager in this league for 20-odd years so I'm sure he will be fighting with his players to put things right.
"And they had a very good victory last night, 3-0, which showed they bounced back and as always it will be a hugely tough game for us because of the quality of their players."
With fixtures ahead against Arsenal, Liverpool, Tottenham, Manchester City and Manchester United, Allardyce's side face the toughest schedule of any of the teams fighting for Premier League survival. Palace saw their four-game winning streak come to an end as they suffered a 3-1 defeat at Southampton on Wednesday.
Injuries have depleted the Palace squad in recent weeks, with midfielder Yohan Cabaye the latest player to join the extensive casualty list due to a calf injury sustained at St Mary's.
Many favour Palace to avoid the drop despite those problems, and Allardyce suspects he knows why, having previously worked his magic with Bolton and Sunderland.
Pointing to the possible reason, he said: "Maybe the past experience that I've had in saving teams in this position and the quality of players we've seen over the last four games hitting their potential in terms of their performance.
"But it is a tough run-in and it's going to go down right to the wire I think.
"It's about who can hold their nerve (that) is normally the big key to success when the pressure is on you at this level. When you go into the single-figure game mark, when that bell starts ringing, the time is running out, you've got to be very brave and stand up and be counted in those situations to survive and be in the Premier League next year.
"I think eight points will be enough.
"I think it's important that we don't lose against Arsenal. It's not arguably that we've got the hardest run-in, we have got the hardest run-in, but we are in good form at the moment so hopefully that form will continue and the results will come with it."