The former Gunners record scorer understands the Netherlands international's desire to move, worrying that the club's frugal business model could leave them behind bigger spenders
The Dutch striker announced earlier in July that he would not be renewing his contract at the Emirates, which has one year left to run, and has been heavily linked with a move to Manchester City.
Club legend Wright, whose record of 185 goals for the Gunners stood for almost eight years before Thierry Henry surpassed the total in 2005, admitted that he could understand the 28-year-old's motivation to leave.
"In many respects, I cannot blame him for wanting to join a club who are winning trophies," Wright told The Sun.
"At least Van Persie is not the sort of player who would be unprofessional and cause problems within the group.
He added, "For the last few years, Arsenal have lost at least one top player each summer and they have struggled to win anything as a result. In previous seasons, Manchester United and Chelsea were the successful teams the top players wanted to join — now, it is City."
Arsenal last won a trophy in 2005, defeating Manchester United in the FA Cup final on penalties, but since then have endured the sale of Patrick Vieira, Thierry Henry, and late last summer the departures of both Cesc Fabregas to Barcelona and Samir Nasri to Manchester City.
The moves came after prolonged speculation and were said to have contributed to the club's poor start the to the season, but the Gunners managed to recover and finish in third place in the Premier League to qualify for the Champions League.
Van Persie was crucial to Arsenal's attack, scoring 37 goals, and Wright commented that the club's progress would be threatened if the pattern was repeated.
He explained: "Arsenal need to address this problem of losing their best players. I admire their business plan about not spending what they haven’t got, but the club is getting left behind.
"Even if Van Persie does leave they have yet another problem as Theo Walcott finds himself in a similar contract situation with just one year left.
"For Wenger, the end of the transfer window cannot come soon enough."