Williams, who eased into the fourth round with a victory over Daniela Hantuchova, and older sister Venus have never returned to the tournament in the California desert after being jeered by spectators in a controversial final in 2001. (Agencies)
The Williams sisters were due to play each other in the semi-finals but Venus pulled out minutes before the match, citing injury.
Spectators vented their displeasure with the late withdrawal during the final, booing 19-year-old Serena in her match against Belgian Kim Clijsters and also jeering her sister and father Richard Williams when the pair arrived to watch the match.
Richard Williams alleged he had heard racist taunts from the crowd and the family have not returned since.
Serena was asked if Mandela's message of reconciliation might have led her to re-consider her boycott.
"It actually crossed my mind a couple days ago, or after I saw the movie," the 32-year-old told reporters at Melbourne Park.
"I thought about it... Right now I don't know. I just have to focus on this tournament.
"But I think Mandela was a really amazing man. I felt really honoured to have a chance to meet him, get to know him a little bit, and get to know his story a little better."
"Mandela: Long Walk to Freedom," a movie about the anti-apartheid hero, opened just days before his death at 95 last month.
Williams reached the fourth round in Melbourne with a dominant 6-3 6-3 win over the 31st-seeded Slovak Hantuchova at Rod Laver Arena on Friday.
She next faces either Australia's Sam Stosur or Serbian Ana Ivanovic, who play in the evening session.
The win was a record 61st for Williams at the Australian Open, putting the American past Australian Margaret Court's 60.
Williams defeated Romania's Irina Spirlea, a former top 10 player, in her Melbourne Park debut in 1998 before being beaten in the second round by Venus.
"Felt good," Williams, who practised on public courts in Compton, a tough inner-city suburb of Los Angeles, said of her first trip Down Under.
"I definitely wanted to be here, and I don't remember my first impressions. As a kid, you don't particularly dream of - especially where I'm from. I never thought I would be in Australia.
"For me, it was a great opportunity to see a land that's so far away that you don't go to even in your dreams."
Williams has won five titles at Melbourne Park since her debut at the year's first grand slam 16 years ago and is a hot favourite to win a sixth after a dominant season last year when she won the French and U.S. Opens.
"I feel like, in life, 32 is young. In sports, it's old," she added.
"But for whatever reason, I feel like I just never was really able to reach my full potential, and I feel like recently I just have been able to do a little better.
"I just keep trying to improve on everything."
Williams has teamed up with Venus for four doubles titles at Melbourne Park, but the celebrated sisters cancelled their bid for a fifth on Friday, with Venus withdrawing due to a leg injury.
Williams, who eased into the fourth round with a victory over Daniela Hantuchova, and older sister Venus have never returned to the tournament in the California desert after being jeered by spectators in a controversial final in 2001.