The Frenchman has come under fire for not buying new players following Saturday's 3-1 defeat at home to Aston Villa, while another fan group, 'The Black Scarf Movement', wrote to chief executive Ivan Gazidis to outline concerns about how the club is run.
Wenger, one of the highest-paid managers in the Premier League, is set to be offered a new contract by the club but the AST want him to be be offered a renewal based on merit, rather than sentiment.
The letter in full:
Arsene Wenger has much to do to earn a new contract at Arsenal
"In recent weeks Ivan Gazidis has spoken of the club's intent to offer Arsene Wenger a new contract. The AST believes this is inappropriate. For now the club's entire focus must be on using the remaining days of the transfer window to strengthen the team significantly.
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"For several transfer windows now Arsenal have not used all the resources available to strengthen the team. Arsenal supporters are dismayed by this continued lack of ambition most notably illustrated when the manager describes fourth place as like a trophy. We do not advocate reckless spending for the sake of it; we advocate proper use of all of the available resources for the benefit of the team.
"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 in the weeks ahead. Considerable improvement must be shown for us to be convinced this should happen and we believe that other senior football appointments must come first.
"There remain important questions about the way player identification, recruitment and remuneration processes are managed at Arsenal. Earlier this summer we presented detailed reports to the club on how it can improve its Boardroom to strengthen our football infrastructure. The failings we highlighted in Arsene Wenger holding far too much power have only been amplified in recent weeks. These must be addressed as a matter of urgency.
"Stan Kroenke does not attend many Arsenal matches nor seem to have the time to devote to the affairs of Arsenal but it is clear to all that football personnel he is ultimately responsible for are [sic] failing. The AST calls on him to appoint an independent expert to conduct a review of all football functions at Arsenal. Clearly the interaction between our scouting, negotiating and player purchasing processes are failing and need urgent improvement."