Maddison, 24, has been linked with a move to the Emirates as Mikel Arteta looks to bolster his squad after a disappointing campaign last season.
Speaking on ITV ahead of the Community Shield between Leicester and Manchester City, Keane said: "Maybe he might just fancy a bit of change, maybe just fancy a bit of London? I don't know.
"It's a difficult one, [Jamie] Vardy had an opportunity to go to Arsenal, he turned it down.
"He got big money, turned it down, he got big money at Leicester, let's not kid ourselves. But Leicester, the group of players they have, they've [also] got a new training ground.
"If he's leaving Leicester, I don't think Arsenal is the right option. If I was him I'd sit tight."
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