The companies are understood to have held informal discussions but they are still at an early stage and no approach has been made to LVMH.
The high profile deal would see Diageo, which owns brands including Guinness, Smirnoff and Baileys, adding the wine and spirits empire of LVMH chairman Bernard Arnault to its stable.
It is rumoured that Diageo, advised by Goldman Sachs, had offered LVMH €10bn, but the French luxury goods company, advised by Lazard, wanted €12bn.
The sale of its drinks division would free up cash for LVMH, which also owns Louis Vuitton, Fendi and Donna Karen, to spend more on the fashion side of its business.
Diageo has seen its position as one of the world's largest drinks groups threatened by European rivals, such as Pernod Ricard.