Wenger believes the 28-year-old can become an all-time great, but helping the Gunners win a trophy this season.
Wenger said: “I loved Arshavin because he has things that are just down to him. He is an intelligent player and he looks like he is a shrewd street player because he creates something always in unexpected situations.
“I believe he has a big challenge in front of him because he made his team in Russia, St Petersburg win, and if he manages to make Arsenal win he will become an all-time great.
“I think we have many players who are in that bracket (with Ronaldo and Messi) and for us it is over a whole season when they can show that.
“That is his real challenge he faces and I am convinced he has all the potential to do it.
“I consider him a great player, but if you want the consideration of everybody else people consider your qualities with trophies.
“But you can say players like Giggs can never win a World Cup because Wales never goes to the world Cup. But he shows in the club he is a great.
“He is a leader and he is a character, believe me. He has something specific to him that he uses well – a low centre of gravity, great pace and tricky dribble.
“He uses all that he has in the locker in an intelligent way and don’t forget he is a winner as well.”