Wenger, 63, is heading towards the final season of his current contract and has been linked with taking charge at big-spending Ligue 1 side Paris St-Germain.
However, after helping guide Arsenal back into a top-four finish in the Barclays Premier League, Gazidis is in no doubt Wenger remains the right man for the club. "We think we have got a fantastic manager. We hope that he wants to do what he is doing for the long term. I believe he does," Gazidis told journalists from the Highbury House board room.
"I think he is still ambitious, still driven and sees the potential of the club as he looks forward and I think he is very excited by that. We have a great relationship and he has a great relationship with the board as well. So, quietly and at the right time I think we will make an announcement on that when things are all put in place."
Wenger has always stated he would honour his contract, and that any negotiations on a possible future deal must not distract from efforts of the team to bring to an end what is fast approaching a decade without silverware. "We have got a lot of confidence in Arsene that he is the right person to take the club forward and I think he will want to do that," Gazidis said.
"We think we have got a fantastic manager who has seen us through moving to a new stadium, which is for many clubs a difficult period, with consistency and so we think we have got the right person to make the kinds of choices and decisions that we are going to have over this really significant period of the club's development."
Despite Arsenal maintaining their remarkable record of finishing within the top four once again, Gazidis accepts that on its own cannot be enough. Arsenal crashed out of the Capital One Cup to Bradford, and then lost in the FA Cup at home to Blackburn, with their European hopes ended by Bayern Munich despite a valiant second-leg win in Germany.
"We want to be competing at the top of the game and in order to do that you have to be in the Champions League, so we are pleased to (have) qualified, or at least, for the qualification games," he said.
"But it is not ultimately where we want to be with moving the club forward. We want to be a club that is competing at the very top end of the game and that means competing to win the Premier League and competing to win the Champions League."
Gazidis added: "The critical thing now as we look ahead over the next season and the season after is our developing financial capability which will give us a lot more options than in recent years."