Cuomo originally unveiled the 1.5 mile tram — which will connect Long Island Rail Road and 7 train riders to the airport — last year.
Months later, he announced plans for a massive renovation of the airport, moving terminals closer to the Grand Central Parkway to add new airplane taxi space.
The renovation plans were prompted, in part, by statements made by Vice President Joe Biden who said the domestic airport resembled a "third world country."
"This is what New York has deserved for a long time and now we are going to get it," Cuomo said in July.
Sources said the Port Authority will need the Iron Triangle's space for parking during the airport project, which is expected to be completed by 2021.
The area is across Flushing Bay from the airport, but would connect to LaGuardia via the AirTrain, which will be accessible across Roosevelt Avenue by the Willets Point 7 train and LIRR station, according to the governor's proposal.
A spokeswoman for Delta, who sources said has been working on the parking proposal, said the company "continues to be closely engaged in the redevelopment of LaGuardia Airport" but referred questions about the proposal to the Port Authority.
The Port Authority did not immediately respond to a request for comment.
Councilwoman Julissa Ferreras-Copeland said she's "eager to work with all who see the value of bringing resources to Corona" and praised the AirTrain for bringing improved transit to her district.
"The transformation of Willets Point is a promising project for this community, and I look forward to working with Gov. Cuomo on his plans to invest here," she said in a statement.
The announcement comes months after Mayor Bill de Blasio and the city withdrew support for part of redevelopment proposal for the industrial area approved under former Mayor Michael Bloomberg.
The administration said they were disappointed by the limited number of affordable housing units in the plan.
"We really want to see significant improvements that would mean that the public would also see a healthy mix of affordable and market rate housing, delivered on a real timeframe," Deputy Mayor Alicia Glen said in August, after they declined to join an appeal with the project developers against a group looking to block the plan.
"We know a lot has gone into this project, and we hope that this team will continue to work towards that goal with us."
It was the latest legal battle for the redevelopment.
In July, a judge from the Appellate Division of State Supreme Court ruled in favor of a group of business owners, advocates and some politicians who have fought against the "Willets West" plan to build a mall on the Citi Field parking lot.
The judge supported the group's argument that the plan violated a state law that protected public parkland.
A month later, the city did not appeal that ruling although developers Queens Development Group did.
The QDG, a joint venture of Sterling Equities and Related Companies, was granted another appeal in November by the state court of appeals.
The plan for Willets Point is in line with Cuomo's focus on infrastructure, recently announcing plans to spend $3 billion to renovate "ugly" Penn Station.
He also announced a proposal to modernize the MTA by expanding Wi-Fi hotspots, providing USB ports on trains, buses and in stations and expedite a new pay system to replace the MetroCard.