One of the sources said the new deal would require approval from Tiffany shareholders, which Tiffany expects should be straightforward. The source added that there would be no restrictions on Tiffany's ability to pay dividends until the deal closes.
LVMH did not respond to requests for comment. Tiffany declined to comment.
The initial deal ran into trouble last month when the French group said it could no longer complete the transaction by a Nov. 24 deadline.
It cited a French political intervention preventing it from doing so, but also what it described as the jeweller's "dismal" performance during the coronavirus crisis.
The two companies have been facing off in a Delaware court, with Tiffany seeking to force LVMH to honour the deal. The case is scheduled to be heard in early January.
The Wall Street Journal earlier reported that the two parties were nearing an agreement to lower the takeover price to $131.5 per share, following weeks of acrimonious exchanges.
Some analysts said they were baffled by the fact that LVMH appeared to have gone to great lengths to achieve what seemed a small discount to the original deal.
"If confirmed, the magnitude of the price tweak would be odd. It is unclear to us why LVMH and its legal team would pursue the course of action they have done since early September to secure a minimal discount to the terms originally agreed," said Flavio Cereda at brokerage Jefferies.
Cereda added however that the business rationale behind the deal remained solid and that Tiffany was "the perfect fit" for Louis Vuitton owner LVMH.
LVMH agreed last year to buy Tiffany in its biggest acquisition yet, betting it could restore the U.S. jeweller's lustre by investing in stores and new collections.
The deal was designed to boost LVMH's smallest business, the jewellery and watch division that is already home to Bulgari and Tag Heuer, and help it expand in one of the fastest-growing industry segments while also strengthening its U.S. presence.
New York-based Tiffany, immortalised in the 1961 movie Breakfast at Tiffany's starring Audrey Hepburn and known for its signature pale blue boxes, retains a resonance as the go-to purveyor of engagement rings that only a handful of rivals can match.
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