Tiffany  (TIF - Get Report) asked French luxury goods giant LVMH (LVMUY) to raise its $14.5 billion acquisition offer, claiming that it significantly undervalues the U.S. jewelry chain, Reuters reported.

Tiffany shares were up slightly to $124.77, while LVMH was off modestly to $88.48.

Tiffany's board decided that LVMH's $120-per-share, all-cash bid was too low to become the basis for negotiations, Reuters reported, citing people familiar with the matter. Tiffany told LVMH it could open its books and provide confidential due diligence if the French luxury company sweetens its offer, Reuters said.

LVMH remains engaged and is considering a new offer. While the exact figure being discussed hasn't been determined, Reuters said that sources have previously said Tiffany's board saw a private level of $140 a share.

The owner of Louis Vuitton, LVMH, which is behind luxury labels such as Christian Dior, Fendi and Givenchy, is eyeing a long-awaited move into the U.S. market. 

Analysts have noted that more than half of Tiffany's sales come from outside the U.S., providing LVMH with both a doorway into the domestic luxury market while supporting the group's growth in key markets such as Europe and China.

LVMH believes Tiffany needs to spend more on reinventing and marketing its brands, and that it can achieve this only as a division of LVMH, Reuters said.

LVMH purchased Bulgari in 2011 and increased its smallest and newest business division, jewelry and watches, which also includes Hublot and Tag Heuer watches.

Acquiring Tiffany would increase LVMH's exposure to the bridal and diamond category, as well as to U.S. luxury shoppers. Should there be a deal, LVMH plans to keep the Bulgari and Tiffany's brands separate, according to Reuters.