The Gunners have lacked a midfield general since the France international moved to Serie A giants Juventus 2005.
Arsenal manager Arsene Wenger has used Mathieu Flamini, Alex Song, Francis Coquelin and Granit Xhaka in a holding role.
However, the Gunners defence has often found itself exposed to undermine Arsenal’s impressive attacking talent.
Wenger is set to stand down at the end of the current campaign following another disappointing season.
Ironically, Vieira is being linked with a potential appointment at the north London club following a stint in charge of Major League Soccer outfit New York City outfit.
Asked where Arsenal need to improve their team in the summer transfer window, Winterburn told BetStars:
“I would love anybody to come into the football club that’s going to excite – as Arsenal supporters, we keep harping back to Patrick Vieira in terms of that type of figure in the centre of midfield.
“We need a dominant midfield player, we need a dominant centre-half and we need a wide left player who can take the ball forward at pace. The Premier League now is all about pace and taking the ball forward and Arsenal need to get that into their squad.
“Those are the type of players in terms of advanced roles that I would be looking at, defensively you’re looking for a powerful, dominant centre-half and an athletic midfield player.”
Arsenal are set to finish in sixth place in the Premier League table to miss out on a place in the Champions League for the second successive campaign.
The Gunners lost 1-0 to Atletico Madrid in the second leg of their Europa League semi-final to end their hopes of winning the competition.
Arsenal haven’t won the Premier League title since 2003-04 when the Gunners finished the season unbeaten.
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