Williams last played at the 2017 Australian Open and won while she was nine weeks pregnant.
Australia's Margaret Court, with 24, is the only player still ahead of Serena in terms of Grand Slam singles titles.
Williams, who gave birth to a daughter in September, could return for the Australian Open next month.
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Mr Khan then visited the Golden Temple complex, where the holiest of Sikh shrines, Harmandir Sahib, is located and offered prayers.
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"She has got her visa, she has entered, she's practicing, and she probably just needs a bit more space for a bigger entourage", tournament head Craig Tiley said.
"There's no question that she'll be ready in our view and she wants to break a record that is Margaret Court's".
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"We'd be pretty excited about the possibility [of her coming]", Tiley said.
Tiley described the Australian Open, which will be held from January 15-28, as a "family-friendly event". "Roger Federer travels with his four kids and we are a family-friendly event", he said, referring to Williams and her baby. Williams recently announced on social media that she has started training again.
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