Wenger is due to meet the Arsenal board later on Tuesday to discuss whether or not he will be extending his 21-year reign as manager.
The 67-year-old Frenchman, who is out of contract next month, has come in for criticism and calls to go from some Arsenal fans during a mixed season which saw the club fail to reach the Champions League for the first time in 19 years but also win the FA Cup.
It remains to be seen if Wenger and Arsenal will sever ties just days after the Gunners beat Chelsea at Wembley claim a record 13th FA Cup success, but Wright believes that could well be the case.
And Arsenal's second-highest goalscorer of all time says it has been "total incompetence" to have allowed this situation to have arisen.
Writing in his column in The Sun, Wright said: "I've got a nasty feeling Arsene Wenger will walk away from the Arsenal job today, leaving the club totally in the lurch.
"And you would have to say it would serve them right, because there has been absolutely no forward planning for the day when he finally left the Emirates.
"The only way the board should have let him run down his contract is if they had private assurances he was staying.
"Otherwise, it is total incompetence to get to this stage."
Wright believes Arsenal should have singled out Wenger's eventual successor some time ago and now fears what the knock-on effect could be if the Frenchman does go at this point, with regards summer planning and transfer activity.
The 53-year-old ex-England international also warned fans of the north London club who are upset at a fifth-placed finish in the Premier League that things could get even worse.
He added: "The next boss should have been identified ages ago and shepherded by Arsene for a season or two, even if he didn't like the idea.
"With no one to step in, it will now be a disaster if Arsene goes. That's why I often tell fans to be careful what you wish for.
"We already face a season in the Europa League - and things could get a lot worse before they start to get better."
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