The Daily Mail are reporting that the Gunners have entered into talks with the centre-half after having been linked with a number of defenders in the summer transfer window.
The same articles states that Champions League runners-up Atletico have placed a £40m price tag on Gimenez in a bid to warn off suitors.
The 21-year-old Uruguay international is thought to have a £56m release clause in his los Rojiblancos contract.
Arsenal endured a disappointing start to the Premier League season after the Gunners suffered a 4-3 defeat by title rivals Liverpool at the Emirates Stadium on Sunday afternoon.
Wenger was forced to start with Calum Chambers and Rob Holding at centre-half following injuries to Per Mertesacker and Gabriel Paulista.
France international Laurent Koscielny was nursing fitness issues as he sat in the stands to watch his team-mates lose a seven-goal thriller to Liverpool.
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