Rory McIlroy -- one of Tiger Woods' best friends on the PGA Tour -- says Tiger is "doing better" after his horrific car crash ... and could be discharged from the hospital in the next week or so.
McIlroy made the revelation on "The Tonight Show Starring Jimmy Fallon" on Tuesday ... saying he's spoken with Tiger since the 45-year-old was seriously injured in a rollover crash on Feb. 23 -- and is getting positive news from the golf legend.
"He's doing better," Rory told Fallon .