The Spaniard launched his campaign to equal the Swiss great's mark by dropping just five games in a 6-2, 6-3, 6-0 annihilation of Bolivian Hugo Dellien in the Australian Open first round, AFP reported.
The Mallorcan, the first man to be world number one in three different decades, can not only match his great rival's achievement, but also become the first man in the Open era to win all four Majors at least twice if he lifts the trophy again at Melbourne Park.
It is a big ask for the 33-year-old Nadal, who has only won the title once before in Australia, against a tearful Federer in 2009, with four runner-up finishes to his name.
"I don't care about 20 or 15 or 16. I just care about trying to keep going, keep enjoying my tennis career," said Nadal.
"It's not like 20 is the number that I need to reach. If I reach 20, fantastic. If I reach 21, better. If I reach 19, super happy about all the things that I did in my tennis career.
"I am very satisfied about my tennis career because I give it all most of the time," he added.
"That's the only thing that matters."
The Australian Open is the only Major Nadal has failed to win more than once, having claimed 12 titles at Roland Garros, four at the US Open and two at Wimbledon.
He has been a finalist in Melbourne four times since winning but has struggled to get over the line, something that baffles him.
"I have been a break up twice in the fifth set and I lost. Another time I have been injured in a final, of course, against a great opponent," he said on why he had not been able to convert in Australia.
"If I am able to reach my highest level, that's the thing that I have to worry about.
"If I am able to play at my highest level, normally I am able to produce some good chances.
"If not, impossible."
Meanwhile, two-time Grand Slam champion Simona Halep survived a couple of tumbles and a sore wrist before surging into the second round on Tuesday.
The Romanian fourth seed recovered from a poor start to beat the American Jennifer Brady 7-6 (7/5), 6-1 and launch her title bid.
The 28-year-old Halep had her serve broken in the first game by the 49th-ranked Brady, who defeated world number one Ashleigh Barty in the buildup to the year's first Grand Slam.
Something to cheer
Australia's Nick Kyrgios put his country's bushfire disaster behind him and gave home fans something to cheer about with a first-round victory on Tuesday.
The 24-year-old overcame Italian Lorenzo Sonego 6-2, 7-6 (7/3), 7-6 (7/1).
"I was just really excited to get out here. Obviously a pretty emotional couple of months for all of us, so I just wanted to come out and put on a good performance," said the Australian, who has never gone beyond the last eight at a Major.
"This is my favorite court in the world... I feel super comfortable. You guys are the best. I feel the support."
Elsewhere, Towering fourth seed Daniil Medvedev navigated a challenging first-round clash against last year's quarterfinalist Frances Tiafoe.
The talented 23-year-old, who won four titles last year and was runner-up at the US Open, ultimately showed his class to outlast the American 6-3, 4-6, 6-4, 6-2 on Rod Laver Arena.
"It was a really tough first match, it was up and down for both of us. A first round is never easy, especially against someone like Frances," said the 6ft. 6in. (198cm) Russian.
"I think I could do many things better, but it is a big win and I'm happy to be through."