LVMH is close to buying U.S. jewelry chain Tiffany & Co. for about $16.3 billion after sweetening its offer, sources said on Sunday, as the owner of Louis Vuitton and Bulgari aims to tap the fast-growing luxury jewelry market.

The two sides are close to an agreement after the French luxury goods company raised its offer price for the company known for its engagement rings and ties to Hollywood glamor to $135 per share, sources familiar with the matter said.

The boards of both companies will be presented with the terms of the deal on Sunday, one source said. A deal could be announced later on Sunday or on Monday, two other sources said.