When asked by TMZ Sports about his status, Gallinari said the thumb is "very good" and that he's "almost ready to play."
Gallinari suffered the injury in July when he punched Jito Kok of the Netherlands while playing in an exhibition game for Italy.
ESPN's Adrian Wojnarowski reported last month that the injury wouldn't require surgery and that Gallinari was expected to be ready for the start of Clippers' training camp in September.
L.A. acquired Gallinari this offseason in a three-team trade that included the Denver Nuggets and Atlanta Hawks. The 29-year-old veteran spent parts of the past seven years with the Nuggets after beginning his career has a member of the New York Knicks.
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Injuries have plagued Gallinari throughout his career, as he has played in 70 or more games in a single season just twice.
He has missed 19 or more games in each of the past four seasons, and sat out the entire 2013-14 campaign with a torn ACL.
Gallinari has been highly productive when on the court, though, as he averaged 18.2 points, 5.2 rebounds and 2.1 assists per game last season while shooting 38.9 percent from beyond the arc, which was his highest mark since his rookie year.
The Italian star will be a key part of a new-look Clippers team that will attempt to stay in the Western Conference's playoff mix despite trading point guard Chris Paul to the Houston Rockets this offseason.