Pique is the founder and President of ports and media investment group Kosmos, who have received approval from the ITF to transform the Davis Cup.
The new plans will see a new annual season-ending World Cup of Tennis Finals that will crown the Davis Cup champions.
It will feature 18 nations and be played over one week in November.
Kosmos have promised significant increases in prize money for players and ITF member nations, and the funding of grass roots projects and other tennis development programmes.
Federer won the Davis Cup in 2014 with Stan Wawrinka and has a great respect for the traditions of the competition.
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And the Swiss star says he doesn’t want the Davis Cup to become the ‘Pique Cup’.
Federer told reporters: “For us tennis players it’s a bit strange to see a footballer come into our world. He should be careful.
“The Davis Cup should not become the Piqué Cup.”
Speaking earlier this month, Pique said tennis needed to change otherwise it risked dying.
He told the BBC: “Sometimes things have to change, or they have the risk to die.
”I can understand for a very traditional tournament like the Davis Cup, it’s difficult for people and they have doubts.
”Everyone agrees that change has to be done, but there are some people who think it needs other changes and that is something I can understand.”
Federer’s comments also come amid speculation Pique could move the new Davis Cup to September.
That would put the tournament in direct competition with the Federer-backed Laver Cup.
In 2019, the Laver Cup will take place in Geneva, Switzerland.