The Daily Star says Bournemouth boss Eddie Howe is the man they have identified to succeed him at the Emirates.
And Gazidis has confirmed to fans that plans are already in place for when Wenger decides to quit.
Gazidis spoke to 17 Arsenal supporters' representatives earlier this month when he revealed the news.
“Ivan Gazidis said that it would be a big challenge when the day arrives that the manager leaves," minutes from the meeting read.
“A lot of work has been done on infrastructure in recent years which will help insulate us when we make that difficult transition.
“He confirmed there is a plan in place but we obviously do not talk about it publicly.
“He reinforced the fact everyone is currently very positive about the direction and looking forward to the season."