The Gunners boss has confirmed that he will stand down as manager of the north London outfit at the end of the 2017-18 season.
Arsenal on the hunt for a new head coach to rebuild the Gunners following a tumultuous couple of seasons under Wenger.
Some big-name coaches such as Massimiliano Allegri, Carlo Ancelotti, Luis Enrique and Thomas Tuchel have been touted as potential replacements.
The British media has speculated over the possibility of a former Arsenal player succeeding Wenger, such as Mikel Arteta, Thierry Henry and Vieira.
The former France midfielder has previously worked as a coach at Manchester City before the World Cup winner took charge of Major League Soccer outfit New York City FC.
Former Arsenal defender Dixon talked up his former team-mate Vieira as a potential replacement for Wenger.
“I would still like to see somebody that’s Arsenal through and through. That would suggest somebody like Patrick (Vieira),” Dixon told ITV Sport.
“He’s obviously inexperienced and there’s a huge amount of work to do there. All the recruitment has to change because they’ve not recruited well enough for me over the last few years. That needs to change and that might be beyond Patrick’s remit. So it’s a really difficult one.”
Arsenal haven’t won the Premier League title since 2003-04 when Vieira captained the Gunners to their famous unbeaten season under Wenger.
The north London side have won the FA Cup in three of the past four seasons but Wenger’s side haven’t reached the Champions League quarter-finals since 2010.
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