Not content with presiding over numerous French fashion and beauty houses - including Christian Dior, Givenchy, Christian Lacroix, Kenzo and Louis Vuitton - Mr Arnault has this week snapped up "5 per cent plus" shares in Gucci, one of Italy's oldest luxury fashion houses. Gucci shares have risen 19 per cent since Tuesday.
Gucci declined to comment on the move, as did LVMH, but, under United States law, the fashion conglomerate is obliged to issue a declaration of intent within the next week or so. Analysts predict that Mr Arnault will mount a full bid for the company before long. Such speculation is fuelled by the fact that, only a week ago, he resigned from the board of Diageo, the British food and drinks company which owns both Burger King and Little Chef. If he were to sell LVMH's 11 per cent share in Diageo, he could raise up to pounds 2.6bn to buy Gucci.
Mr Arnault has had his eye on Gucci for some time. The company represents one of the great fashion success stories of the decade. Less than four years ago, it was facing bankruptcy, worth only $250m (pounds 1.52m) and beleaguered by in-fighting and intrigue. When the young American designer Tom Ford - said to be a close personal friend of Mr Arnault - was brought in to re-vamp the label, sales doubled, then doubled again. Gucci now boasts sales of $2.2bn worldwide.
It is thought that as far back as 1995, when Gucci went public, LVMH bought a small stake in the company anonymously, as part of its policy to invest in rivals to secure access to shareholder information. Next, inspired by Ford's success, in October 1996 Mr Arnault moved the young British designer John Galliano to the ailing house of Givenchy in the hope that he could do the same thing. It worked. Exactly one year later, Mr Arnault moved Galliano across to Dior, and installed Alexander McQueen at Givenchy. Sales at both houses are said to be booming - despite the economic crisis in Asia which caused a 50 per cent drop in LVMH share prices.
But Mr Arnault is not the only person with his eye on Gucci. Last summer Gucci's arch-rival, Prada, acquired a 5 per cent stake in the company and soon afterwards took another 4.5 per cent, making it the label's largest shareholder.
When asked at that time whether he would be able to resist stepping into the fray, Mr Arnault said: "Gucci is a remarkable company which has had excellent growth. For our part, LVMH has a strategy aimed at strengthening our presence in the US and Europe. All kinds of opportunities present themselves."