The Daily Star says the Dutchman is wanted by Manchester United but the Italians are now weighing up a bid for the 29-year-old, who is out of contract next summer.
Vlaar was a key man for Holland at the World Cup, helping them to a third-place finish in Brazil.
But his future remains in doubt with Villa yet to offer him a new deal, despite plans to.
The Italians are prepared to offer Vlaar a three-year contract, and believe he could be tempted to join them.
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