The Gunners boss signed a new two-year contract with the north London club in the summer despite the disappointment if missing out on a top-four spot last term.
Arsenal finished in fifth place in the Premier League table but won the FA Cup thanks to a 2-1 win against title holders Chelsea to appease their disgruntled supporters.
The north London side were 2-0 winners against Tottenham Hotspur in the derby last weekend in a rare committed performance from the Gunners against one of their big rivals.
However, Arsenal have lost four of their last six games in the Premier League following defeats at Stoke City, Liverpool, Watford and runaway leaders Manchester City.
Ajax coach Dennis Bergkamp, New York City FC boss Patrick Vieira and Belgium assistant manager Thierry Henry have all been touted as potential candidates to replace Wenger.
Former Arsenal defender Keown believes Van Bronckhorst has shown some promising potential at PSV but suggested he would need some more experience before replacing Wenger.
“When he was a player, I didn’t see him becoming a manager. Of the Dutch, I thought Dennis Bergkamp would become a manager more than him,” Keown told the Daily Mail.
“Van Bronckhorst is a very determined individual. I watched his Feyenoord side play against Manchester City on Tuesday and it was a massive improvement in their performance from the 4-0 loss at home to City in September.
“He’s having a difficult season. They are seventh in the Dutch league, and have won one game in their last nine in all competitions. We will have to wait about Arsenal. It is still a way off.”
Arsenal are in sixth place in the Premier League table.
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