Beckham, who has been living in a hotel since joining AC Milan on loan in December, is disillusioned with members of the public and photographers hanging around outside.
The 30-room Villa Oleandra is just 39 miles from Milan - and Beckham is already well acquainted with it having stayed there with his wife as Clooney's guests last year.
Italian media reported that Beckham, 34, had told friends:
'I have fallen in love with the beautiful countryside. It's peaceful, quiet and near Milan. It would be great for the family.'
The Beckhams' friendship with Clooney has made them favourites to get the villa, which is on the market for £20million.
Clooney, 48, bought the villa( below) in the town of Laglio for £10million in 2002.
The Beckhams already own a £14million house in Beverly Hills (shown below) , where Mrs Beckham, 35, and their three children have lived during his loan from LA Galaxy.
They also own 'Beckingham Palace' (shown below) in Hertfordshire and a home in France.
Property prices around Laglio have shot up since Clooney bought the villa at Laglio on Lake Como and which has it's own private jetty into the water, swimming pool, gym, tennis courts and beautifully manicured gardens.