LONDON—David Beckham’s possible jump to AC Milan could be more than just a temporary deal and might mean “arrivederci” to the Posh ’n Becks show in America.

Beckham needs to stay competitive to keep his spot on the England team, and the loan would come with Major League Soccer in its offseason.

AC Milan vice president Adriano Galliani said Wednesday a deal is close. Beckham would join the Italian club in January and play in Serie A for a few months before returning to the Los Angeles Galaxy.

But there could be more to Beckham’s move to Milan, a glamorous cit...

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