updated 04/18/2009 AT 9:25 AM ET
•originally published 04/18/2009 AT 9:05 AM ET
Is Uma Thurman going to walk the aisle this weekend? Sources close to the actress and her fiancé, multimillionaire Arpad Busson, who arrived on the Bahamian island of Eleuthera earlier this week, tell PEOPLE that wedding plans may be underway for as early as Saturday.
The couple announced their engagement last June after Busson presented Thurman with some serious bling: an eight-carat diamond surrounded by 20 smaller stones.
Thurman, 39, and Busson, 46, have been spotted at a luxury resort on Eleuthera.
According to marriage requirements for the Bahamas, the couple must be in the country for at least 48 hours to obtain a marriage license. Licenses are issued by the Registrar General, the same official who issued a marriage license to Mariah Carey and Nick Cannon last year.
The Registrar General’s office declined to comment on whether they have issued a marriage license.
If the couple do exchange vows, it will be the third marriage for Thurman, who has a son and daughter with her ex (since 2004), Ethan Hawke. Her marriage to Gary Oldman ended in 1992. Busson has two sons with former supermodel Elle Macpherson, from whom he split in 2005.