The 24-time Grand Slam champion won 10 of the first 11 games and threatened to inflict the most lopsided defeat on Nadal in the 60th meeting between the pair, before eventually winning 6-1, 6-4.
Nadal said after the loss that he would decide on his future in the sport after the Olympics, where he is also playing in the doubles with Carlos Alcaraz.
But Djokovic, who played Nadal for the first time when they were still teenagers at the 2006 French Open, told reporters he would like to keep the rivalry going.
"There's no other rivalry in the history of tennis that's had 60 matches between the two players. So I think that itself makes it very, very unique and very special," said Djokovic.
"I just hope for the sake of our rivalry and the sport in general that we'll get to face each other once or maybe a few times, on different surfaces, in different parts of the world, because I feel like it can only benefit the sport.
"I don't know how he feels in his body, what his plans are, but let's hope we can play some more."
Djokovic said only time would tell if Monday's match would turn out to be the last time he played Nadal.
"We don't know that. It really depends on many different factors," he said.
"I mean, it depends on whether both of us will keep going or whether we're going to participate in the same tournaments or not.
"I think we both want to play in the Grand Slams and the biggest tournaments. I don't know. We'll probably be very selective."
No 'brotherhood'
Their careers will be forever inextricably linked, but Djokovic played down the notion of a "brotherhood" with Nadal while acknowledging his deep respect and admiration for the Spaniard.
"It's tough to be close, honestly greatest rivals, and you don't want to maybe give insights to your life or the way you feel and stuff because that can maybe expose you and stuff," said Djokovic.
"I guess that's one of the reasons why maybe we didn't connect so close and I don't think at that level you can really connect so close to anybody, but who knows when the career ends for both of us.
"It's a long life hopefully for both of us, and we're both family people and hopefully we can address the different side of our relationship and reflect on things that we went through together, that we lived together, the special moments in a different way."
Djokovic's victory avenged his loss to Nadal in the semi-finals of the 2008 Olympics, when the Serbian had to settle for bronze on his debut.
"It was an incredible match, just the anticipation and the hype around this match was huge," said Djokovic.
"I'd probably say there's even more tension playing him at the Olympic Games, just because there is that element of representing your country and being part of the Olympic Games, which is so rare - it only happens every four years."
