"I've had no indication from any shareholders that they are about to launch a takeover," he told the BBC.
"We're very comfortable with the multi-ownership model. If that were ever to change, we'd have to address the situation at that time."
"You never know what fortune holds for you, but we believe we have a squad that will be very much in the mix for any competition we enter over the next five years.
"There is no question in my mind that this club is going to be very successful in delivering trophies to its fans consistently in that time period."
Wenger, 60, is under contract until the end of next season but Gazidis had no concerns about the Frenchman's future with the north London club.
"We are very relaxed about Arsene's contract," he said.
"At the right time we and Arsene will talk about extending that. Typically with Arsene those discussions happen towards the end of the contract period. But we're extraordinarily happy with him.
"It's difficult for me to imagine anything other than Arsene leading the team forward with this young group of players. There's a huge amount of ambition left in Arsene and a huge amount of vision and legacy that has yet to be achieved."
