The Wall Street Journal said Beijing and Havana secretly agreed on the facility, some 100 miles off Florida. The Cuban government denied the "unfounded" reports, while the White House said it wasn't "accurate."
The new policy represents a major change to US immigration rules, with President Joe Biden telling migrants: "Do not just show up at the border."
The embassy will offer legal pathways for Cubans to visit the US as Washington deals with a massive wave of illegal immigrants from the island nation.
The Dry Tortugas National Park in Florida has been shut indefinitely as authorities struggled with migrants arriving in boats. There has been a rise in migrants arriving from Cuba due to the economic turmoil there.