The boards of the luxury firms have been discussing a potential deal since last month, and will meet on Sunday to approve the deal, sources tell CNBC's David Faber.
An agreement could be announced as soon as Monday.
Shares of Tiffany, the iconic New York-based jeweler, have risen over hopes of a higher priced deal. Shares closed on Friday at $125.51. They had traded at about $140 in the middle of last year.
Jewelry was one of the strongest performing areas of the luxury industry in 2018, according to consultancy Bain & Co, which forecast that comparable sales in the $20 billion global market were set to grow 7% this year.
Tiffany, founded in New York in 1837 and featured in the 1961 movie "Breakfast at Tiffany's," has struggled with growth over the last several years. It experienced falling annual sales and profit since 2015, before a revenue turnaround in 2017.
The jeweler has also pushed an expansion into China, but experienced a decline in sales in the U.S. and Asia from factors like the U.S.-China trade war.
Analysts at Credit Suisse and Cowen say Tiffany could be worth roughly $140-$160 per share.
Paris-based LMVH has about $50 billion in annual revenue from brands including Louis Vuitton and Dom Perignon. Acquiring Tiffany would give LVMH exposure to the bridal and diamond category and to more U.S. luxury customers.
LVMH plans to keep the Bulgari and Tiffany's brands separate if the deal materializes. The company's primary rivals, including Gucci-owner Kering and Switzerland's Richemont, which owns Cartier, are also increasing their exposure to high-end jewelry.
The Financial Times first reported news that LVMH and Tiffany reached a deal.
Correction: An earlier version misspelled Dom Perignon.