L.A. Clippers forward Danilo Gallinari tells TMZ Sports the thumb he busted while punching a guy in Italy is healing nicely ... he's almost ready play again!
The 28-year-old suffered the injury last month -- right after he signed his 3-year $65 million deal -- when he socked a player from the Netherlands during a European exhibition game for Italy.
The good news ... Gallinari says the thumb is "very good" -- and he expects to use it to help the Clippers win a championship this year!