The interaction came ahead of the Premier League giants' clash at the Emirates Stadium on Sunday evening.
Arsenal have claimed seven points from a possible nine in their first three matches of the season.
United on the other hand have fared slightly worse as they fell to a 2-0 defeat to Tottenham in their second game.
Having finished second last season, the Gunners know a win will be key to boosting their chances of winning the Premier League title.
As a result of their major progress, former star Walcott believes Mikel Arteta's side are currently superior to their Sunday opponents.
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When asked by Micah Richards on Sky Sports who is the bigger club right now, he initially said: "That's a stupid question."
However, he went on to say: "Arsenal finished above United so if you go right now, for me, I would have to say them. I feel like they're bit more organised, especially behind the scenes as well."
Keane was not one to agree with him though and jumped to the defence of his former, with whom he won seven league titles.
Patting Walcott on the back with a smile, he said to him: "You're so naive and young huh? So naive and young."
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The ex-Arsenal winner did in fact add: "If you're talking overall, then United definitely top that."
Richards then asked Keane if United were bigger than Arsenal and was met with a very simple response: "Of course."
Both teams have cemented themselves as two of English football's most successful sides, although United's 67 major trophies trump Arsenal's 48.
You can follow live updates of the highly anticipated match on our live blog.