Tottenham defender is swaying over West Brom move, while Crystal Palace consider bid.
Wimmer has been strongly linked with a move to the Baggies with Spurs set to sign Ajax defender Davinson Sanchez.
West Brom had reportedly earmarked him to play at left-back as well as at centre-back.
Crystal Palace have now entered the chase for his services as Frank de Boer seeks to strengthen after a disappointing opening two games.
The Austrian defender has proved a capable stand in for Tottenham in the Premier League, but head coach Mauricio Pochettino has refused to hand him a more prominent role, and even last season preferred to use Eric Dier when required.
Wimmer would be a coup for either West Brom or Palace, but Tottenham are demanding a high price.
The Times reports they are offering him around to clubs in an attempt to try and fetch their desired £20 million price tag.
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