The duo have 35 major titles and more than US$200 million ($274 million) in career prize money between them.
Nadal admitted it would be "amazing" to finally play alongside his great rival, though the selection has not yet been confirmed by Borg.
"We've talked about that years ago, to play in some tournament together. It didn't happen yet. We're looking forward to playing here, hopefully. Let's see if the captain allows us to play."
Joining Federer and Nadal in the Europe team are fellow top 10 players Marin Cilic, Alexander Zverev, and Dominic Thiem with former No 4 Tomas Berdych making up the squad.
Team World, skippered by John McEnroe, features four Americans - Frances Tiafoe, Sam Querrey, John Isner and Jack Sock as well as Australian crowd puller Nick Kyrgios and Canadian teenager Denis Shapovalov.
Tiafoe, who gave Federer a scare at the US Open, was a late call-up for Juan Martin del Potro.
The three-day tournament runs from Friday to Sunday and will feature three sets per match, the last of which is a super tie-break (10 points).
There are four matches a day - three singles and a doubles.
Nadal, who added the US Open to his Roland Garros title earlier this month, said he may be a little ring-rusty over the weekend having taken a break following his New York triumph.
"I didn't practice here yet, of course after the US Open. After a big event, you go down a little bit, you need to recover energy. I have today and tomorrow to practice hard and let's see then," said the Spaniard.
Ironically, the Laver Cup presentation took place on Wednesday in Prague's old town on the same day that tennis's flagship team event, the Davis Cup was holding its draw for the 2018 season.
Last weekend, the semifinals and playoffs for this year's Davis Cup took place but without the likes of Federer who opted out of Switzerland's tie against Belarus.
The Davis Cup schedule has come in for a constant stream of criticism from top players wary of adding more pressure to their calendars.
