Wenger has a contract at Arsenal until the end of next season but this term has been one of his most testing since joining the club in 1996.
The Gunners sit sixth in the Premier League table, are already out of the title race and are set to lose Alexis Sanchez to Manchester United.
Mesut Ozil and Jack Wilshere are also out of contract in the summer.
A section of Arsenal fans are calling for Wenger.
But the Frenchman insisted he will not quit in a defiant speech during his press conference today.
“No, that’s not the way I respond,” he said when asked if this would be his last season at Arsenal.
“2018 until now has not been very positive but what’s important is how we respond.
“My personal situation is a bit secondary to that.
“It’s difficult at the moment but very exciting.
“We have to get over this transfer period because for us this period has been more unsettling than ever.”
Arsenal have not won the league since 2004 and were it not for three FA Cups in four years Wenger may already have been forced out the Emirates door.
The Gunners broke their transfer record in the summer to sign Alexandre Lacazette – but Wenger is notoriously frugal when recruiting new players.
United, meanwhile, will offer Alexis Sanchez £500,000 a week and have spent almost £300m on new players since Jose Mourinho took charge in 2016.
And Wenger concedes Arsenal cannot compete in the market with their Premier League rivals.
“Financially yes,” he said. “That doesn’t mean we can’t compete on the pitch.
“We did the maximum we could afford to do [to keep Sanchez].”