The 32-year-old Spanish midfielder was named in the role on a permanent basis at the start of the season following the departure of Thomas Vermaelen.
But former Gunners midfielder Parlour believes World Cup winner Per Mertesacker would be a more suitable candidate for the prestigious job.
“I think it should be Mertersacker as captain to be honest,” Parlour wrote on Sportlobster.com.
“But I’m looking for leaders all over the pitch, we haven’t had that for a long. Tonight we had more shape, more discipline because they played as a team.”
Parlour is confident despite Arsenal’s mixed start to the season that Wenger’s side can secure their perennial top-four finish and Champions League football.
Asked where he felt the north London club would finish this season, Parlour replied: “Top four but not top two. So many clubs vying for that position.”
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