The Gunners have been linked with a big-money move to sign the Schalke 04 midfielder before the end of the month, but Keown has said that the French coach will bide his time before signing the highly-rated German international.
"If Arsenal are going to buy a player now, it's got to be a ready-made player, like Mesut Ozil was," the 47-year-old told talkSPORT.
"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."
The North London side are currently one point clear of Manchester City at the top of the Premier League table.