The former centre-back believes that Wenger would be better placed to make the bid in the summer when he may be able to land the 20-year-old at a significantly lower price than Schalke's £35 million valuation.
Speaking to talkSPORT, Keown said: "If Arsenal are going to buy a player now, it's got to be a ready-made player, like Mesut Ozil.
"Wenger is the sort of manager who deals himself a hand at the start of the season, and then plays it.
"He doesn't like dipping in [to the market in January]. They'll be saving their money for an Ozil-like signing in the summer."
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