The New York-based club, due to enter the second-tier USL Championship in 2021, are part-owned by Villa, with Gombau, 43, reportedly being targeted as inaugural head coach.
The pair forged a friendship when involved in the A-League back in 2014 - Villa as a Melbourne City guest marquee and Gombau during his tenure at Adelaide United.
On departing the Reds, Gombau briefly linked with Villa, then at MLS outfit New York City FC, to help set up Villa’s US-based DV7 Soccer Academy.
The one-time Socceroos assistant and ex-Olyroos chief, who also coached Western Sydney Wanderers, declined to return calls from The World Game after this week officially cutting ties with Indian Super League Odisha FC.
The former Barcelona youth coach guided the rebranded club to a sixth-place finish this season - his second at the club - just missing out on the playoffs.
He was offered a two-year contract extension.
However, the lure of linking up with Spain’s FIFA World Cup-winning all-time leading scorer looks to have proved irresistible.
Citing “familial reasons”, Odisha FC’s President Rohan Sharma said of Gombau’s exit: “Some things in life are more important than football.
"I’d like to thank coach Gombau and his coaching staff from the bottom of my heart for all that they have done for the club.”
Gombau told reporters: “It wasn't an easy decision to make. I have enjoyed my time at Odisha and I am proud of what I built there.
“It is with some regret that I can't finish what I started, but I will always be rooting for the success of Odisha FC.”
The USL, which comprises 35 teams, is currently suspended for a month - along with the MLS - due to the coronavirus outbreak.
Villa, 38, announced his retirement after winning Japan’s Emperor’s Cup knockout tournament on New Year’s Day with Vissel Kobe - alongside his old teammate Andres Iniesta.
In addition to his part ownership of Queensboro, he will have a technical role at the club, though he plans to be largely based in Spain.
