A disappointing transfer window and 3-1 loss to Aston Villa in their opening game of the Premier League season on Saturday has Arsenal fans fearing their side may struggle this season.
In a statement, the Arsenal Supporters' Trust (AST) said there was no need to offer Wenger a new deal just yet.
"Chief executive Ivan Gazidis has spoken of the intent to offer Wenger a new contract. We believe this is inappropriate," the statement read.
"The entire focus must be on using the remaining days of the transfer window to strengthen the team significantly."
Arsenal last won a trophy in 2005 and were expected to spend big in the off-season, but are yet to pay for a player.
They have had several bids for Luis Suarez rejected after failing to meet Liverpool's valuation of the Uruguayan striker.
"Ambitious football clubs invest the money they receive from their fans, and sometimes their owners, to make themselves stronger," the AST statement read.
"Arsenal supporters pay some of the highest ticket prices in world football, providing the club with considerable financial resources, but the ambition and ability to use them appear to be missing.
"The fact that there is money available for squad-strengthening is not disputed. The AST's independent analysis suggests that the amount is somewhere between £70million and £100million."
The supporters also called on Arsenal's American owner Stan Kroenke to appoint 'an independent expert to conduct a review of all football functions' at the club.
"A decision on whether to offer an extension to the manager's contract, which ends in May 2014, should only be taken following the closing of the transfer window and assessment of the team's performances," the AST said.
"Considerable improvement must be shown for us to be convinced this should happen."
