The 67-year-old has been in charge of the Gunners since 1996, but his current contract at the Emirates Stadium expires at the end of the current campaign.
Calls for him to step down from his role have grown in recent years, with the club having failed to win the Premier League title since 2004.
Wednesday night's 5-1 defeat at the hands of Bayern Munich resulted in more questions being asked over his future, with the Gunners set to be eliminated in the last 16 of the Champions League for the seventh consecutive season.
It is understood that the club have offered Wenger a two-year contract extension which remains on the table, but he will reportedly wait until the summer to decide whether to extend his stay.
Any decision is expected to be a mutual agreement between the club and Wenger once the Frenchman has assessed the campaign and whether he can take the club any further.