Wenger signed a two-year contract extension this summer despite growing calls for him to leave Arsenal.
The Frenchman has been in charge of the club since 1996 but there is supporter unrest as they club seek to win their first title since 2004.
Arsenal have got off to a poor start in the Premier League, losing two of their first three games.
They also struggled in the transfer market and face losing Alexis Sanchez and Mesut Ozil on free deals next summer.
And Wenger says he considered his position before signing the contract.
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“Yes, I hesitated to extend for personal reasons,” he told French TV station Telefoot.
“I’ve been at Arsenal for 20 years and I’m always wondering if I should continue to lead the club.
“That we have started quite badly this season (isn’t good).”
Arsenal beat Leicester 4-3 at the start of the campaign but have since lost to Stoke and Liverpool.
“It is a very difficult start to the season because we started with a home game that won at the end with a good performance.
“The second game was pretty good but not very effective, and the third we had a catastrophic performance. It raises many questions and questions.”
Yet Wenger insists his side can still challenge for honours this term – even though they are already six points off the top of the table.
“Despite all of this the team has real potential and we must recover as always in times of crisis and we must win the next game,” he said.