It is understood former Tottenham winger Bale and his partner Emma have viewed the property, which is said to be worth £1million, in the Spanish capital's exclusive La Moraleja district, reports the Daily Mail.
But the £86million world record signing, who scored on his debut in Saturday's 2-2 draw at Villarreal, will view other properties before making a decision.
The house has been put on the market after Ozil's £42m move to Arsenal.
Bale and his family are currently staying in the upmarket Sheraton Mirasierra Suites Hotel, in north Madrid.
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