The remarks from Lee’s daughter Shannon are the latest amid an ongoing row over the acclaimed director’s portrayal of her father in his latest movie, Once Upon A Time…In Hollywood.
In the black comedy – which was released in cinemas on Wednesday – Lee is portrayed as arrogant, to the annoyance of his family and friends.
Tarantino has defended the portrayal of the Asian-American actor, who is played in the film by actor Mike Moh.
But Lee’s daughter told Variety: “He could shut up about it. That would be really nice. Or he could apologise or he could say, ‘I don’t really know what Bruce Lee was like. I just wrote it for my movie. But that shouldn’t be taken as how he really was’.”
In one scene, a cocky Lee gets into a best-of-three fight with Brad Pitt’s character, a stuntman named Cliff Booth, after the pair fire insults at each other.
Lee is seen to win the first round, but is slammed into a vehicle in the second. The third never manages to get under way.
Tarantino has stood by the portrayal.
“Bruce Lee was kind of an arrogant guy,” the acclaimed filmmaker said at a press junket in Moscow earlier this month.
“I didn’t just make a lot of that up. I heard him say things like that, to that effect.
“People are saying ‘Well, he never said he could beat up Muhammad Ali.’ Uh, yeah, he did. Not only did he say that, his wife, Linda Lee, said that.
“In the first biography I ever read was Linda Lee’s Bruce Lee: The Man Only I Knew, and she absolutely said it.”
Speaking to The Wrap last month, Ms Lee said she found it “disheartening” to see her father portrayed on screen as “an arrogant a****** who was full of hot air”.
She added: “What I’m interested in is raising the consciousness of who Bruce Lee was as a human being and how he lived his life.
“All of that was flushed down the toilet in this portrayal, and made my father into this arrogant punching bag.”
She is not the only person to come to the defence of the martial arts legend.
His protégé and training partner Dan Inosanto has said the actor “was never, in my opinion, cocky”.
Also speaking to Variety – about the alleged comments about Muhammad Ali – Mr Inosanto said: “Bruce Lee would have never said anything derogatory about Muhammad Ali because he worshipped the ground Muhammad Ali walked on.”
He added: “In fact, he was into boxing more so than martial arts.”