Nadal created history by defeating Russian Daniil Medvedev in the Australian Open final to claim a men's record 21st major title and move one ahead of Federer and Novak Djokovic, who were both missing in Melbourne.
The Spaniard, who has twice played at the Laver Cup, paired up with Federer for their first and only doubles match together at the inaugural edition of the event in Prague in 2017.
"I suggested to Roger we should play doubles together in London and he seems keen, so now we just need to persuade our captain Bjorn (Borg)," said Nadal.
Federer has not played since being knocked out in last year's Wimbledon quarter-finals following a third knee surgery, but the Swiss great aims to return by April or May.
Photo: Getty Caption: Rafael Nadal and Roger Federer at the World Tour Finals in 2013.