The two have clashed in the past, most notably when Bolton Wanderers earned a string of victories over the Londoners while under the reign of Allardyce.
The duo will face off on Wednesday night when the Gunners host the Hammers at the Emirates Stadium, and Allardyce concedes that he does not always see eye to eye with the Frenchman.
"We don't get on," admitted Allardyce. "I think way back we had some tussles.
"If we beat Arsenal in the past it was because of the long ball, or we used to get labelled physical.
"It was a frustration that used to make me really enjoy the fact that we had beaten an Arsenal team with a Thierry Henry and a Patrick Vieira and players like that."
Arsenal beat West Ham 3-1 at Upton Park earlier in the season.