The two powerhouses currently occupy the top two positions in the Premier League and Parlour believes that his former club Arsenal, Liverpool, Manchester United and Tottenham Hotspur will be left to scrap for the remaining two Champions League spots.
He told talkSPORT: "Chelsea grind out results. They're so clinical in the way they get results and Manchester City stand a great chance, particularly if Sergio Aguero can keep playing like that [against Spurs].
"You look at Manchester City and Chelsea and they're in a different league compared to Arsenal.
"They're so far above Manchester United, Liverpool, Arsenal and Spurs. I think all these teams are fighting for two places, they're fighting for third and fourth."
Parlour made 339 appearances in a 14-year career with the Gunners and is fondly remembered for scoring a 30-yard strike in the 2-0 FA Cup final win over Chelsea in 2002.