Wenger, 67, has been in charge of the Gunners for nearly 21 years but may miss out on Champions League football for the first time if Arsenal can not overtake Liverpool or Manchester City on Sunday.
Asked when the board meeting is scheduled for, Wenger replied: "I think it is after the FA Cup final".
The board may also prefer to keep Wenger on at the club with many of Europe's top mangers already in employment. One of those is what happens with the manager, the players coming in and contract renewals. "If I leave tomorrow Arsenal Football Club I have no right to come back, because I have worked here", Wenger said.
"The board meeting is after the FA Cup final".
That will mean Alexis leaves the club according to reports, with the forward unhappy at the prospect of missing out on Champions League football, and hardly short of suitors. Chelsea and Tottenham are confirmed to finish first and second, leaving Manchester City, Liverpool and Arsenal to battle for third and fourth.
Arsenal has been playing well lately, winning four straight league games, but its rebound may have come too late.
Celtics' Gerald Green after loss: 'We've been in this situation before'
James played just 33 minutes - a low for this postseason and just the second time he played fewer than 40 in the 2017 playoffs. One thing the Celtics would love to bring to the table is more offense from Isaiah Thomas.
It really is out of the Gunners hands whether they qualify for the Champions League next season.
Arsenal chiefs have been eager to enforce a shake-up of Wenger's back room staff, as well as the appointment of an influential figure who will assist in the recruitment of players and overseen contract negotiations. We are professional and we want to win. If we don't win the game I'll be sad.
Everton manager Ronald Koeman has enjoyed four victories over Arsenal since moving to England with Southampton in 2014, losing only once in six encounters, and he hopes his good run will continue.
Koeman has no new injuries worries, but remains without Maarten Stekelenburg (groin), Seamus Coleman (broken leg), Ramiro Funes Mori (knee), James McCarthy (hamstring), Aaron Lennon (stress-related illness) and Yannick Bolasie (knee).
The Gunners have failed to mount a serious title challenge in recent seasons and have not won the Premier League title since their famous unbeaten triumph in the 2003-04 season. And though I modified that in the final article, it didn't go down well. It is not like some players have never left the club.
Our former captain and defender Adams has revealed that he regularly spoke out about Arsene's methods while he was with the club, and ended his chances of working at the club again once his playing days were up. "So, it's sad. For me it's a subject of no interest, and so I would like to dedicate my time to something that is more interesting".