The singer-and-actress and husband Marc Anthony – who were both born in New York to families from Puerto Rico - want to build a state-of-the-art soundstage in Fajardo to attract more major movies and television shows to the US island.
According to Fajardo's mayor, Anibal Melendez, the couple had a "lot of enthusiasm" for the project when he met with them recently in Miami, Florida.
The proposals are said to still be in their infancy and it is unknown when work on the scheme would be expected to begin.
Last year it was claimed the couple – who have two-year-old twins Max and Emme together – wanted to buy property in Puerto Rico after a brief holiday in the self-governing territory.
Jennifer, 41, and Marc, also 41, were said to have been so impressed with their visit to Trump's International Gulf Club Puerto Rico during their trip they considered splashing out on a home there.