The world number one and sister Venus have not played at the March tournament in the American desert since 2001, when they were subjected to heckling and, allegedly, racist abuse.
The crowd turned against the Americans after Venus pulled out of a scheduled semi-final clash with Serena, who was then booed during the final against Kim Clijsters.
They have resisted all calls to put the past behind them, but Serena revealed she had considered the issue after watching the Nelson Mandela biopic Long Walk To Freedom.
She said: "It actually crossed my mind a couple days ago, after I saw the movie. I thought about it."
On the court, the world number one was not too troubled on another punishing hot day in Melbourne, beating Daniela Hantuchova 6-3 6-3.
It was Serena's 61st win in the singles main draw at the Australian Open, more than any other woman.
There were reports that the 32-year-old had declined to do a TV interview after the match because she felt dizzy, but she denied that was the case.
Serena said: "I didn't feel dizzy. I had some pressing things I needed to take care of.
"I feel good to have got through that one because it was tough conditions out there, but I was happy to win."
She had been due to play doubles as well on Friday but withdrew from the tournament because of an injury to Venus.
"I love playing doubles, love playing with Venus, but sometimes it doesn't work out," said Serena. "We'll make sure we come back and play, maybe next year."
Teenager Eugenie Bouchard continued her run with a dominant 6-2 6-2 victory over America's Lauren Davis.
It is the first time the 19-year-old Canadian, the WTA's newcomer of the year in 2013, has reached the fourth round at a grand slam.
Ninth seed Angelique Kerber is also through after a 6-3 6-4 win over America's Alison Riske and next meets Italian Flavia Pennetta, a 6-1 7-5 winner over Mona Barthel.
Russian Ekaterina Makarova, a quarter-finalist the last two years, is one win away from matching that after a 6-4 6-4 victory against Monica Niculescu.
Makarova will next meet fourth seed Li Na, who saved a match point on her way to a battling 1-6 7-6 (7/2) 6-3 victory over Lucie Safarova.
Li, beaten by Victoria Azarenka in the final last year, made 18 unforced errors and hit just two winners in the first set and looked in deep trouble in the second.
Czech Safarova served for the match at 5-3 and then held a match point at 6-5 but missed a backhand by a fraction.
The pair took a 10-minute break before the third set because of the extreme heat and initially that looked to have unsettled Li again but she was the stronger at the end, clinching victory after two hours and 37 minutes.