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 and with it another shot at the Champions League, Gazidis is in no doubt Wenger remains the right man to take the club forward as they prepare to strengthen the squad during the summer for a long-overdue sustained assault on the title next season.
"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 board room of Highbury House.
"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 since Patrick Vieira lifted the FA Cup in 2005.
While careful not to be drawn on any timescale, Gazidis indicated the vibes were positive.
"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," he said.