The goalkeeper has been suggested as a possible long-term replacement for Mikel Arteta.
The goalkeeper has proved to be an astute signing by Arsene Wenger in the summer, with many believing he has transformed them into genuine title contenders.
There is now talk that Cech could be named captain next season, with the current wearer of the armband Mikel Arteta looking likely to leave the club in the summer.
And Parlour has admitted that he would have no issue should their current number one be named as his permanent replacement, ahead of current vice-captain Per Mertesacker.
“I wouldn’t have a problem with him being captain,” he told Talksport. “Ideally, I would have a centre half as captain but at least you know Cech would play every game.
“He’s been very not just on the pitch, but off it as well. He’s very important in the dressing room. Having that level of professional in the dressing room have very important for Arsenal this season.”
Cech would certainly be the wise option for Wenger to name as his new skipper next season, given his current stature in the squad.
Mertesacker has enjoyed a fine season in the heart of the defence alongside Laurent Koscielny, but many expect him to lose that place at some point in the near future with Gabriel Paulista waiting in the wings.
Cech though is surely guaranteed his place for the next few years at least based on the impact he has had this season, making him an ideal replacement on the basis of playing time alone.