Arshavin impressed on Friday night as Russia managed a 4-1 win over the Czech Republic in Euro 2012 Group A.
The 31-year-old has failed to impress at Arsenal, since joining the club in a £16million deal from Zenit St Petersburg in 2009.
Arshavin spent the last six months of this season on loan at his former club Zenit.
“You could say that he was played in the wrong position at Arsenal,” Parlour told TalkSport.
“Arsene Wenger’s always played him on the left hand side and he’s more of a central player.
“I’m sure Arsene will be watching and wondering why he couldn’t do that for Arsenal. He never played like that which is frustrating for the fans, Arsene Wenger and the players.”
“Let’s see what happens with him,” he added. “I’m not sure whether he’ll go back to Arsenal or they’ll try and sell him.”
