(Reuters) - LVMH LVMH.PA is close to buying U.S. jewelry chain Tiffany & Co TIF.N 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.

A Tiffany & Co. logo is seen outside a store in Paris, France, November 22, 2019. REUTERS/Gonzalo Fuentes

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.

It would be LVMH’s largest takeover.

The new price is up from $130 last week and $15 higher than the original all-cash offer delivered to Tiffany by LVMH managing director Antonio Belloni on Oct. 18.

It represents a 7.5% premium over Tiffany’s closing share price on Friday and is more than 50% higher than where the price stood before LVMH launched its effort to woo the company.

The two companies did not immediately respond to requests for comment.

Aside from the price tag, the terms are not known.

LVMH, owned by Europe’s richest man, Bernard Arnault, has eyed the company for years after buying Italy’s Bulgari in 2011 for 3.7 billion euros, at the time the largest luxury goods deal in a decade.

Tiffany will help grow its smallest business, give it a bigger share of the lucrative U.S. market and expand in jewelry, the fastest-growing sector in the luxury goods industry.

Known for its signature robin’s egg blue packaging, Tiffany rebuffed LVMH’s initial advance made just five weeks ago, arguing it significantly undervalued the company.

Reuters reported this week that LVMH had persuaded Tiffany to provide it with confidential due diligence after it raised its bid to $130 per share, worth almost $16 billion.

The news of Sunday’s boosted offer was first reported by the Financial Times.

Tiffany, founded in New York in 1837 and featured in the 1961 movie “Breakfast at Tiffany’s” starring Audrey Hepburn, had struggled with falling annual sales and profit since 2015, before a revenue turnaround in 2017.

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.

Under Chief Executive Alessandro Bogliolo, former head of fashion firm Diesel and a Bulgari alumnus, Tiffany has been building up its e-commerce business and is trying to court younger shoppers with more affordable pendants, earrings and new designs.

(GRAPHIC: Jewelry market growth outpaces other luxury sectors - tmsnrt.rs/31RaK7N)