The speculation turns out to have some basis in reality: Lee seriously contemplated a match between himself and the heavyweight champion. Lee studied Ali's fights carefully. In the book "The Making of Enter the Dragon," director Robert Clause says Bruce Lee talked about fighting Ali back in 1973:
At that time, there were many people who debated about what would happen if Ali crossed paths with Lee. Some people thought Lee would be able to dominate Ali in a fight, while others argued Ali would knock Lee out easily. According to Clause, Lee considered both sides of the argument and even practiced fighting Ali by using a full-length mirror. His conclusion? He probably wouldn't have stood a chance....“Everybody says I must fight Ali some day.” Bruce said, “I’m studying every move he makes. I’m getting to know how he thinks and moves.” Bruce knew he could never win a fight against Ali. “Look at my hand,” he said. “That’s a little Chinese hand. He’d kill me."
But many experts think that with no gloves and no rules, Lee could've done serious damage to Ali. Martial artist Freddie Lee argues street fighting and boxing are completely different, and boxers' limitations are actually a disadvantage when they're not in the ring. Bruce Lee could kick and damage Ali's knees, shins, groin, or face before the heavyweight could even reach him. Ali just wasn't trained to kick or grapple.
Ethan Wolff-Mann points out that Lee was mostly a teacher, not a fighter.
[Lee] didn't have a ton of experience taking punches to the face. Compared to MMA guys or boxers who constantly take damage points during their fights, Bruce avoided—wisely—getting bashed around. If someone with some mass hit him... Street fights might be short, but there's a lot of time on that clock in the ring.
In a boxing ring, with gloves, and going 15 rounds? Most experts say Ali would crush Lee. But in a street fight with no rules, where you're allowed to damage your opponent in any way you can? Lee could use his kicking and grappling skills to devastating effect. If he could keep Ali from reaching him with his hands, Lee would stand a chance.
Let's be real here. Pure boxing rules, Muhammad Ali hands down. MMA rules, Bruce Lee without question.