(Bloomberg) –LVMH is close to a deal to buy Tiffany & Co., the fabled U.S. jeweler, for more than $16 billion as it seeks to clinch what would be Chairman Bernard Arnault’s biggest-ever takeover.

The French luxury conglomerate’s new proposal — at $135 a share — is 12.5% above the initial $120-a-share bid, according to people familiar with the matter. Both companies’ boards are meeting Sunday to approve the latest offer and an agreement could be announced as soon as Monday, the people said, asking not to be identified because the details are private.

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It’s not the first time that LVMH has raised its bid for Tiffany, a 182-year-old brand known for its robin’s egg blue boxes. Arnault — Europe’s richest person — sought to woo Tiffany, which would expand LVMH’s access to U.S. luxury shoppers, with an increased $130 bid just days ago, people with knowledge of the situation said at the time. But some analysts had predicted the firm could go for an even higher price, with targets of $140 at Credit Suisse and even $160 at Cowen.

Tiffany’s shares have traded steadily above the initial offer price since Bloomberg News first reported the talks Oct. 26, closing at $125.51 a share on Nov. 22.

After a difficult period during which the U.S. jeweler lost track of consumer trends, Tiffany is looking to bounce back by cutting its entry-priced gifting options and revamping its marketing to target younger shoppers. For LVMH, the brand would help the Louis Vuitton owner challenge Cartier owner Richemont for dominance in the global jewelry business.

While LVMH — which oversees Christian Dior fashion, Bulgari jewelry and Dom Perignon Champagne — dwarfs Tiffany with sales of more than $50 billion, the French giant isn’t as dominant in jewelry as it is in fashion or cosmetics.

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Adding Tiffany would expand its selection of more accessible offerings, such as $165 heart-shaped earrings, as well as top-end options like a $165,000 diamond chain.