Both the Gunners and the Toffees recorded important wins on Sunday, as the north Londoners beat West Ham 2-1, whilst Frank Lampard's side shocked Chelsea with a 1-0 win at Goodison Park.
This leaves both sides in good positions heading into the final few games of the season - which culminates in the two facing each other at the Emirates Stadium.
And Parlour believes the two could come to some sort of unspoken agreement which would see them both achieve their respective objectives this campaign.
"It's Arsenal vs Everton on the last game of the season," Parlour told talkSPORT.
"Arsenal need a point [to secure a place in the top four] and Everton need a point to stay up.
"It'll be a 0-0 draw! 'You stay in your half, we'll stay in our half!'"
It's something O'Hara recalls happened when his Wolves side faced Blackburn in 2011.
He revealed he even begged Morten Gamst Pedersen to put a free-kick 'in the stands' during a final day of the season clash when both teams needed a point to stay up.
O'Hara added: "I've actually had that. We played Blackburn and we both needed a point to stay up.
"They scored, then we scored, and then I remember Pedersen had a free-kick in like the 80th minute and I was like, 'Mate, just put this in the stand! What are you doing?'
"He's stepping up to try and rifle one in the top corner!
"We literally played out like a training ground friendly for the last 10 minutes. We were like, 'Ref, blow up, blow up'."
O'Hara - who scored in the game - and his Wolves side managed to survive relegation from the Premier League that day, despite losing 3-2 at Molineux.
Whether that could happen this season remains to be seen, but it's something that the likes of Tottenham, Burnley, and Leeds wouldn't be too happy about.