Talks on the proposal have been held between Moscow and Abu Dhabi state investment fund Mubadala, The National newspaper reported citing Russian Industry Minister Denis Manturov.
Manturov, who was visiting Abu Dhabi to participate in a military exhibition, said Russia would invest at least USD 200 million in the project.
He said Cuba planned to convert a former military base into "a big airport hub for Latin America".
The project could also include redeveloping a seaport and constructing a railway line.
The newspaper said that Russia was trying to boost its ties with trading partners in the Middle East, Asia and Latin America in the face of international sanctions over the Ukraine conflict.
In December, US President Barack Obama and Cuba's Raul Castro announced their two nations would begin normalising ties, ending a half-century of enmity between the former Cold War foes.
