The former Arsenal striker was analysing the club’s 3-1 loss to Swansea on Tuesday when the topic changed to Wenger’s future.
Wright has always backed the Frenchman, who he played under in north London, but he thinks his time in charge should come to an end soon.
However, the pundit seems to have inside information that the manager will remain at the helm for another two years.
That would take Wenger up until 2020 when he will be 70 years old.
Wright also highlighted problems in the boardroom for the club’s current struggle.
“They [the players] seem to be not responding to this manager at the moment,” Wright told Match of the Day.
“I have been very loyal and I know that Arsene Wenger will probably be there for another two years.
“You know that there is things going on in the background with [Sven] Mislintat and [Raul] Sanllehi and [Ivan] Gsaazidis and you know that there’s a war going on.
“There has been a lot going on and I would like to see [Stan] Kroenke come over and actually get the people to get together and work for the club.”
Arsenal are sixth in the Premier League table and look likely to miss out on the Champions League places.
And Wright blames the inconsistency of performances for their league position.
“You see how the guys can play when they want to like against Chelsea and we’ve seen in certain games, against Man Utd and that, they raise their game,” Wright added.
“When you look at them, it’s the inconsistency of the performances.”