The Gunners have started the process of identifying replacements for the Russian attacker, with Barcelona star Bojan Krkic and Shakhtar Donetsk forward Willian being considered as potential targets.
Arshavin has frustrated Wenger with below-par displays in another season for the north London club that is set to end without a trophy.
The 29-year-old joined Arsenal from Zenit St Petersburg for around £15 million in January 2009 and enjoyed a promising start to his career at the club.
But he has endured a mixed season, scoring just six goals in 34 Premier League appearances and being demoted to the substitutes' bench 11 times as he has struggled to influence games.
Zenit sporting director Igor Korneev has suggested he would be eager to bring Arshavin back to the Russian club, saying: "If his situation at Arsenal does not improve and he's not comfortable in London, we can study this issue in time for next season."
Wenger is a long-term admirer of Bojan, who has failed to establish himself as a regular in the Barcelona side and plays in the wide attacking role currently occupied by Arshavin.
The 20-year-old, who is currently sidelined with a knee injury, will seek talks with the Barcelona hierarchy at the end of the season before making a decision on his future.
The Spain international is under contract until 2015 but wants first-team football to develop his career after making just seven league starts and scoring only three goals for the Catalan giants so far this season.
The striker understands his chances will be limited with Lionel Messi, David Villa and Pedro ahead of him in the pecking order at Camp Nou, while the January arrival of Ibrahim Afellay has nudged Bojan even further down the pecking order.
Bojan has previously revealed his admiration for the Premier League and has been linked with a £15m move to Liverpool as well as Italian side Napoli.
An alternative target for Arsenal could be Brazilian star Willian, who is being monitored by top clubs across Europe including Chelsea and Barcelona.
After four seasons with the Ukrainian champions he is desperate to move to a major European league but Shakhtar would have to lower their £20m price tag to tempt Wenger into a summer bid.
The Gunners believe they could land the 22-year-old with a £15m offer and fellow Brazilian Denilson has encouraged the club to bring his countryman to the Emirates Stadium.
"Willian would be perfect for Arsenal,” Denilson said last month.
“I know him well from the national youth team and he had a real winning mentality even then.
“I've heard Chelsea are interested in him but I think his character could really improve our team. We need match-winners at Arsenal and knowing what he does I know he could do the same in England.
“I believe his style would fit much better at Arsenal because of the way we play football. He's definitely one of the best creative players I have played with.
“I've spoken to him and told him that he could be a success with us. I think he would definitely make our team stronger."