The "machine planet", also called "V'Ger's planet", was an unnamed planet located in an unknown region of space, populated by a species of "living machines". When the NASA Voyager 6 probe fell into a supposed black hole in the early-21st century, it reemerged in this planet's local vicinity, where it fell into the planet's gravitational field. The probe was discovered, repaired, and extensively expanded by the machine race, transforming it into the V'ger artificial organism. (Star Trek: The Motion Picture)
Though the location of the machine planet was never revealed, Will Decker speculated that Voyager 6 emerged on the "far side of the galaxy", which would place the location of this planet in either the Gamma or Delta Quadrant.
According to the Star Trek Chronology, 2nd ed., p. 23, after the Star Trek: The Next Generation episode "Q Who" was produced, it was "half jokingly speculated" by Gene Roddenberry that the machine planet "might have been the Borg homeworld." This idea also appeared in the non-canon novel The Return. The nature of the Borg homeworld has not been revealed onscreen in any Star Trek series, although Captain Jonathan Archer speculated in ENT: "Regeneration" that it might be located in the Delta Quadrant.
If V'ger indeed recorded information on "whole galaxies" while on its return voyage to Earth, as Spock's voiceover indicated, the planet could theoretically be well outside the Milky Way Galaxy.