A number of managers have been touted for the position but Arsenal legend, Ian Wright has proposed another: Sean Dyche.
Wright identified Dyche as Wenger's successor but has questioned whether the north London club would appoint him.
Arsenal have struggled to challenge for the Premier League in recent times and with competition now so tough, many fans wanted Wenger replaced last summer.
He told the BBC, "I believe he is somebody that needs to go, at some stage, to the next level".
"Yeah. The fact is would they give Sean Dyche that job?"
"But I don't think they are as far as that".
Lauren won two Premier League crowns and three FA Cups under Arsene Wenger's stewardship but has ruled out the Frenchman ending his 14-year drought without a league championship.
Those results have also led to Stoke midfielder Charlie Adam calling for Dyche to be given a top job. "If he's got the right attributes he can coach anybody".
He told reporters: "If Barcelona want to join the Premier League, it makes it even more hard to win the title!" He's done his groundwork with relatively smaller teams and got them set up well.
But the man who scored 185 for the Gunners fears the club will not even consider the Dyche because he is not a glamorous appointment.
"He's got the attributes to manage one of the top clubs".
However, Wright is not confident that he would get the job at Arsenal as they are likely to go in for a more established name when Wenger decides to call it a day. "If Arsenal want him they should take him".
'We're so bereft of any manager that's good enough, that can take on the England job.