Barcelona's Pique reportedly met ATP officials this week to discuss a 16-team knockout competition played in one venue over 10 days.
World number one Murray said: "If it comes off, I think it would be a very, very good thing for tennis."
The current Davis Cup format is played over four weekends throughout the year.
Murray, Nadal and Djokovic have all led their nations to Davis Cup glory but have also opted out of playing in the tournament in order to focus on Grand Slam preparations.
Nadal, a 14-time Grand Slam winner, has backed fellow Spaniard Pique's plans and has criticised the International Tennis Federation (ITF) for the Davis Cup schedule.
He said: "For many years they have been static. They haven't moved with the times or looked for new solutions.
"Pique is part of a group that wants to create a World Cup that would be a great and very interesting tournament to compete in."
The ITF has told the BBC: "Our focus is not on what other bodies are trying to do, but in successfully delivering Davis Cup as the world cup of tennis to millions of fans in over 120 nations each year.
"A number of significant changes to the competition's structure, prize money and format will be voted on by all tennis nations at the ITF AGM in August."
The BBC has also contacted the ATP for a response.
World number two Djokovic has warned Pique of the "complex" structure of the sport's governing bodies, but added: "To see one of the football greats coming to the tennis world and trying to support it personally, but also in some structural business way, can only bring positives to our sport."
Later this year the first Laver Cup tournament will also be contested, a Ryder Cup-style competition which will pit a European team featuring Roger Federer and Nadal against a rest of the world side.
The Laver Cup will be played in Prague from September 22-24.
Andy Murray, Rafael Nadal and Novak Djokovic have backed footballer Gerard Pique's plans for a tennis 'World Cup' which could rival the Davis Cup.