Schneiderlin is reportedly attracting interest from Arsenal and north London rivals Tottenham and Parlour thinks Wenger should act decisively to lure his fellow Frenchman to the Emirates Stadium.
"Arsenal need to get Morgan Schneiderlin if he's available in the summer," Parlour told talkSPORT.
"He would be perfect. He's a little bit like Gilberto Silva when he was at Arsenal.
"He can sit back into the back four and, when it's wide, he can be another centre-half. That's so good if you can do that. He's so comfortable on the ball and someone like him would be a great addition."
Arsenal exited the UEFA Champions League last 16 on Tuesday at the hands of Monaco on away goals, leaving Wenger to focus on the FA Cup and Premier League.
Seven points separate league leaders Chelsea and third-placed Arsenal with nine games remaining, but, whatever happens this season, Parlour insists his old club have plenty of work to do to become consistent title challengers again.
He added: "There has to be big investment at Arsenal this summer.
"The Premier League is more important than the Champions League.
"In Europe, sometimes, you need a bit of luck along the way but the league doesn't lie. The most consistent team always win it, that’s what they've got to look at.
"They need to be challenging Chelsea and Man City, along with Liverpool and Manchester United next season."
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