The potential deal, which could be announced as early as Friday, would value Belmond's equity at about $2.6 billion, the Journal reported, citing people familiar with the matter.
The reported price would represent a premium of more-than 40 percent to the close of Belmond's shares on the New York Stock Exchange on Thursday.
Including debt, Belmond's enterprise value would be about $3.2 billion, the WSJ said.
Belmond declined to comment, while LVMH was not immediately available.
(Reporting by Ismail Shakil in Bengaluru; Editing by Sandra Maler)