Unidentified sources close to the couple, who are engaged, said the couple may get married as early as Saturday after arriving on the Bahamian island of Eleuthera days earlier, People.com said.
Bahamas law requires a couple to spend a minimum of 48 hours in the country before it can obtain a marriage license.
The Registrar General's office of the Bahamas would not comment regarding recent marriage license approvals.
Thurman, 39, and Busson, 46, announced their engagement last June with the "Kill Bill" actress showing off an eight-carat diamond engagement ring.
People.com said the couple's marriage would mark the third for Thurman, who previously was married to actors Ethan Hawke and Gary Oldman.