Gazidis refused to say whether Wenger would help find his successor but insisted the club had never been "better prepared" for his decision to leave.
"If he's happy with the decision, I'm really happy and I hope he doesn't retire from football".
Rodgers has revived his reputation in nearly two years in Scotland after a troubled end to his three-and-a-half years at Liverpool in 2015, leading Celtic to the brink of back-to-back domestic trebles in Scotland.
He has also proved to be tactically flexible down the years and will design the best fit for the players left to him rather than cram them into a particular philosophy - a charge often levelled at Wenger.
Wenger did rebuild with a younger and less physical style of player and how close he came to an achievement that would have surpassed everything else is often forgotten.
Winning the European competition guarantees them a place in next year's UEFA Champions League and that is now the North Londoners' primary aim.
Celtic manager Brendan Rodgers.
And given the humdrum seasons of late, the incoming manager will satisfy a joy-starved fanbase with a mere top-four finish in the Premier League. That is what we call perspective.
April 20th, 2018 saw the man who achieved the 'invincible' in 2004, confirm that he will be leaving the club on completion of the ongoing Premier League season. 22 years at one club.
Paris Saint-Germain coach Unai Emery believes that departing Arsenal boss Arsene Wenger could one day manage the French club.
Javier Hernandez has had to show his quality from the bench this season, scoring eight goals with very little game time overall.
"We miss him a lot". But there are enough reports from people in the know to suggest Stan Kroenke's loyalty to Wenger had finally run out. Few, if any. And now the Emirates packs a good 60,000. Week in. Week out.
Former Arsenal captains Robin van Persie and Cesc Fabregas, who both played under Wenger, described the coach as a "father figure".
In it, Wenger said: 'After careful consideration and following discussions with the club, I feel it is the right time for me to step down at the end of the season. It is understood he is not shy of offering an opinion on tactics and team matters there and has been a vital link between manager and squad.
We lived through the Tony Adams and Martin Keown farewells, the Barcelona blow in the Champions League, the moving blues, Thierry Henry, Ashley Cole, Cesc Fabregas, Robin van Persie, Samir Nasri and Alexis Sanchez's departures.