Gazidis, who will receive a grilling from fans at a meeting with the Arsenal Supporters' Trust today, also gave his backing to manager Arsene Wenger and suggested the Frenchman will stay beyond the length of his existing contract, which expires next summer.
Arsenal have already got to work on bolstering their squad for next season, signing Swiss midfielder Granit Xhaka for £30m.
And Gazidis hinted at more to come from Arsenal, who were named wealthiest club in London this week.
"We are in a position that we were not in four or five years ago where we don't have to sell our best players," Gazidis told the Telegraph.
"We can go and sign world-class players if and when the manager identifies them."
Despite finishing second last season, Arsenal's highest league finish for 11 years last season, many fans were left frustrated by their team's failure to take advantage of rivals' misfortune and win the league title.
Many have called for a summer spending spree as the necessary corrective after the Gunners were the only club in Europe not to sign an outfield player last season.
Yet Gazidis has suggested Leicester's title-winning success proved it was not just big-name players who could push a club forward, but also backroom staff such as scouts and fitness experts.
The former Major League Soccer commissioner said: "What is clear is that the big spending was not the solution to all problems.
"It was clever spending and a lot of 'difference makers' underneath the surface".