Honduran Foreign Minister Lisandro Rosales said that negotiations with the United States could make Cuban migrants passing through the Central American country seek refuge in Honduras.
Such arrangements are known as "safe third country" agreements and are part of a larger effort by President Donald Trump to reduce the flow of migrants into the United States.
Rosales, however, rejected that term.
"One of the topics discussed in the deal with the United States is precisely that if Cuban migrants are interested in seeking political asylum ... they do so in Honduras," Rosales told reporters.
Despite talking of a deal, Rosales said negotiations were still ongoing. He said that over the past year thousands of Cubans had crossed Honduras on their way north to the U.S. border.
The United States has persuaded Guatemala to become a safe third country that would accept U.S.-bound asylum-seekers, although the deal has yet to be ratified by Guatemala's government.