World number one Nadal won the US Open by defeating South Africa's Kevin Anderson in a win that marked his 16th Grand Slam title — just three behind number two-ranked Federer's tally of 19.
With the duo looking likely to compete for the top spot in the ATP tennis rankings in the remaining months of the season, Federer is instead focused on an exhibition event in the Laver Cup.
The competition is in honour of 11-time major champion Rod Laver and will see Europe, captained by Björn Borg, take on the rest of the world, captained by John McEnroe.
"For me to spend time with Bjorn, it's quite rare," Federer said, as quoted on Tennis World USA. "He doesn't spend so much time on the tour. When he shows up, it's short."
"I feel every minute you get with him is a privilege. Here we are, he's going to be stuck with us. So it's going, I think, to be very special for all of us, particularly me.
"I mean, I have incredible respect for him. I feel like if I could play one player ever going back, I feel like it would be Bjorn. I feel he's that incredibly good, for what he did for the game. If I look how he played, what he brought to it, it's crazy."
The Swiss ace then turned his attention to Nadal, stating how for once, he can actually be on the same side as the Spaniard, having previously mentioned his desire to be a doubles partner with him in the three-day event.
"So okay, enough of Bjorn. But Rafa [Nadal], he's been such a wonderful champion and a good friend of mine on the tour, one of my big rivals for life, that it's just nice to be able to spend some time with him and support him," Federer added.
"If I can help him, great. If he can help me, even better. Finally, after all these years, I get a chance to actually support his forehand, his aggressive play, his everything, his fighting spirit. Everything before was always like, ahh, another forehand and another fighter."
The inaugural Laver Cup takes place from 22 to 24 September and will be held every year except for an Olympics year.
Both teams will consist of six players and there will be four matches each day, with at least one doubles match.
Click here to see the full rules of the Laver Cup.