The Frenchman, who has been at the helm in North London for the past 21 years, is facing increasing calls from the club's fanbase to depart when his current deal expires this summer.
Protests have grown in recent months following another disappointing campaign, which could still end on a relative high with victory over Chelsea at Wembley Stadium on May 27.
When asked what the meeting will consist of, he told reporters: "I don't know. There are many aspects of a football club which has to be discussed at a board meeting. One of those is what happens with the manager."
Arsenal are still battling to keep their impressive record of qualifying for the Champions League in each of Wenger's full seasons in charge, requiring victory over Everton on Sunday and other results to go their way.