The Atletico Madrid forward has lit up Euro 2016 so far, scoring six times to help les Bleus reach the final ahead of tonight's showpiece with Portugal in Paris.
The 25-year-old also looks to have forged an excellent understanding with international colleague and Arsenal striker Olivier Giroud.
Everton marksman Romelu Lukaku has been linked with a big-money switch to the Gunners, according to The Sun, but Parlour, who won three league titles with the North London outfit, would prefer to see the Atletico hitman join his former side instead.
“Romelu Lukaku’s been mentioned,” Parlour told Sky Sports News. “We’d love to see Antoine Griezmann at Arsenal. That’s the sort of quality they need.”
The Everton man certainly seems the more realistic of the two at the moment.
The truth is that Griezmann's stock is just far too high at the moment, meaning he is well out of Arsenal's price range.
It would also appear unlikely that he is to leave the Spanish this giants this summer, having only extended his contract until 2021 back in June.
Arsenal definitely need a striker. Giroud is an excellent goalscorer, but he simply cannot be relied upon to find the net on a regular basis from August to May.
Everton's Romelu Lukaku looks dejected