Twenty-times Grand Slam champion Federer has said that he is unlikely to play in the new-look tournament, spearheaded by Barcelona player Pique's investment group Kosmos.
Changes to the Davis Cup format will see the 118-year-old competition turned into a week-long event taking place in November, with the first two editions happening in Madrid in 2019 and 2020.
Speaking in August, Federer questioned why Spain defender Pique was "meddling" in the tennis calendar.
"It's a team competition which represents their countries," Pique said. "So the perfect draw in order to have the best players is impossible to have basically because there are top players who will not classify and they can't participate in the tournament. We want to focus on the teams and that's what we did with the wild cards (for Argentina and England).
World number two Djokovic has said he would "prioritise" playing in the ATP's World Team Cup, set to take place in January 2020. He has also criticised the timing of the new Davis Cup.
"I took advantage to have a word with him (Djokovic), as I have done many times, because as you would understand Novak is the head of the ATP Players Council, which represents the players, and to reach an agreement between ATP and the players he is key on this," Pique said.
"The meeting went really good and as he explained after the final he won in Shanghai, the Davis Cup is part of tennis history and history should not be changed. I think we are on the right path, we have to keep talking but I'm very confident that we can reach an agreement."
The World Team Cup has put men's governing body the ATP on a collision course with the International Tennis Federation (ITF), the governing body behind the revamped Davis Cup format.
"I had a dream a long time ago, two or three years ago, and it was to create a unique event in the tennis world in which players could represent their nations and federations," Pique said.
"And at the end, we came to the conclusion that going in hand with the ITF which is the institution that represents all the country's federations globally, it was the best solution."
