Beckham recently ended his long spell with Major League Soccer (MLS) side Los Angeles Galaxy but has not yet announced his next destination.
Rumours of a return to Milan, where he played on loan on two separate occasions in 2009 and 2010, have, however, gathered pace in recent days.
Gazzetta dello Sport carried a report on Wednesday that claimed bookmakers in England had slashed the odds of Beckham returning to the Rossoneri.
The report cited no one from the club but speculated that Beckham would be a welcome addition to Massimiliano Allegri's squad, especially for European fixtures.
Milan sits seventh in Serie A, but is in the UEFA Champions League and will meet Barcelona in the last 16 knockout phase next month.
The seven-time European champion has made no official comment on the reports.