The second longest-serving manager in the history of the Premier League, Wenger is out of contract at the end of the season.
He has not won the league title since 2004, and calls for him to end his association with Arsenal have grown louder since the team's 5-1 Champions League thrashing at Bayern Munich on Wednesday.
That first-leg defeat is almost certain to condemn Arsenal to their seventh successive Champions League exit at the competition's first knockout stage.
"I will decide (my) future in March or April, but I don't (exactly) know when," Wenger told a news conference on Friday, before his team's fifth-round FA Cup clash away to non-league Sutton United on Monday.
"I speak to the board, but I don't want to speak about how they view my future. What's important is the club, not my future. No matter what happens, I will manage next season, whether it is here or somewhere else. That is for sure."
Arsenal have consistently qualified for Europe's elite club competition, but their failure to progress has become a millstone around Wenger's neck.
Their inability to turn promising domestic season starts into sustained title challenges has also left him vulnerable to criticism, and former players are now joining in a chorus of disapproval.
Former Arsenal captain Martin Keown described Wednesday's defeat as Wenger's "lowest point", while ex-defender Lee Dixon added: "This team is getting no response from him. I've never seen him like that."
With Arsenal fourth in the Premier League table and trailing leaders Chelsea by 10 points with 13 games to play, the FA Cup appears once again to be the North London club's last hope for silverware this season.
It was the subject of Wenger's future, however, that dominated the manager's news conference.
"We have to focus on the real problems and they are the way we play football, not my future ... Even if I go, Arsenal will not win every single game in the future," he said.
"I think what is important is that the club makes the right decision for the future."
Wenger, who may be without injured defender Laurent Koscielny for the cup tie, denied reports of a dressing room bust-up after the defeat at Bayern's Allianz Arena.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Larry King)
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