The six-time US Open champion progressed to the semi-finals at Flushing Meadows after beating Karolina Plitsova 6-4, 6-3 in the last eight.
Film director, producer, writer and actor compared watching Williams to watching Muhammad Ali or Michael Jordan at the peak of their careers.
Ali was influential, not just in the boxing ring, but outside of it as he refused to take part in national service.
Following retirement at age 39, Ali focused on religion and charity before passing away in 2016.
And Williams wants to create a legacy similar to that of the former heavyweight world champion.
“To be compared to Ali or Jordan, I really have no words,” Williams said immediately after her victory over Plitsova.
“Mainly Ali, because he did so much for the sport, he did so much for the world, for everyone.
“That’s what I want to do and want to be remembered for.
“It’s not what I want to do on court, but how I can inspire people off the court, that’s my dream.”
Williams will now face Anastasija Sevastova in the semi-finals of the US Open as she hunts for her seventh title in New York.
The 36-year-old has been beaten in the last four three times, including the last two times she has participated.
Williams missed the 2017 US Open as she gave birth but is aiming to get back on top of the world.
But first a clash with Sevastova.
Williams added: “I want to be able to get past the semis here, I’ve had a couple of rough ones.”
Williams was a break down in the first set against Plitsova before reeling off eight games in a row.
She is now just two wins shy of a record-equalling 24th Grand Slam title.