The Frenchman, under contract at the Emirates until 2019, is under increasing pressure after his team's abject display in Sunday's 3-0 League Cup defeat against Manchester City -- their sixth loss in 12 games this year.
Arsenal are 10 points adrift of fourth-placed Tottenham in the Premier League and look likely to miss out on Champions League football for the second consecutive season.
"There are excuses (from Wenger) and he is mollycoddling a team," Wright told BBC radio.
Wright also had harsh words for American owner Stan Kroenke.
"The owner has to take a lot of blame for this," he said. "Kroenke does not care. If he cared, Wenger would not have got a two-year deal.
"Everyone else can start to see that is it getting to a point where Wenger needs to go. The owner has to be here, find out what is happening, how is this working, what are we going to do, how are we going to get back to where the fans want us to be.
Wright's comments follow stinging assessments from the club's record goalscorer Thierry Henry and former Manchester United and England defender Gary Neville, who labelled Arsenal's performance against City "spineless".
Britain's Daily Telegraph newspaper reported that Wenger's position would be reviewed at the end of the season but said that Monaco manager Leonardo Jardim and former captain Mikel Arteta were among replacements being considered.
The Sun said Celtic boss Brendan Rodgers, Arteta and Germany head coach Joachim Loew were at the head of a seven-man list.
But Wright urged caution over appointing the man who overtook him as the club's all-time leading goalscorer.
"Arsenal are not in a position where they can go from someone like Arsene Wenger, who we love so much, yet who you mention to some people in the fan base and their faces screw up.
"They are so angry. I would not want that to happen to Thierry, because he has taken the job straight after Wenger.
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