The main question circulating is exactly where would the tunnel connect along Westchester's northern Sound Shore, which includes the communities of Port Chester, Rye and Mamaroneck.
A new Long Sound crossing has been considered on the Island since 1938 with multiple ideas dumped by fierce community opposition.
Cuomo's administration issued a formal request for proposals to the construction industry and private-equity investors, urging them to express interest in building a tunnel from Long Island.
The request focuses on a tunnel ending in Westchester County and not Connecticut, where the state had also studied as a potential landing spot.
A state-funded study found the tunnel could cost up to $55.4 billion.
"We are taking another step to advance an ambitious project that would reduce traffic on the impossibly congested Long Island Expressway, improve connectivity, and help ensure the region's future economic competitiveness," Cuomo said in a statement.
Click here to follow Daily Voice Peekskill and receive free news updates.