Renowned surgeon Orava performed a minor miracle in fixing Peter Fill's Achilles in good time for last month's Winter Olympics after the Italian skier injured himself in October.
However, Beckham has even less time before the World Cup and has largely been a substitute under England coach Fabio 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 although Tottenham's Aaron Lennon is currently injured.
(Writing by Mark Meadows in Milan; additional reporting by Martyn Herman in London, Editing by John O'Brien and Justin Palmer)