Beckham is due to return to Galaxy in July but Galliani said the Italian club would love to have him back again next season.
"In the dressing room I hugged him and told him that he could stay with us again next year if he wants," Galliani told Sky television.
Renowned surgeon Orava performed a minor miracle in fixing Alpine skier Peter Fill's Achilles in time for last month's Winter Olympics after the Italian injured himself in October.
However, Beckham has even less time before the World Cup and has largely been a substitute under Capello, who has many other options on the right wing.
Theo Walcott, Shaun Wright-Phillips and James Milner are among the players able to play there, Tottenham's Aaron Lennon is another option but is currently injured.
(Writing by Mark Meadows in Milan; Additional reporting by Martyn Herman in London; Editing by Ed Osmond)