The Armani designer clothing label is said to be worth some £1.5 billion and the health of its owner looks like its deteriorating.
Giorgio Armani is 75-years-old and has recently suffered ill-health after contracting hepatitis.
The Telegraph reported that this lack of a clear succession plan is common among the luxury fashion industry in Italy and that no plans around who might take over at Armani have been released publically.
Luca Biondolillo, senior vice-president of international communications at Luxottica Group, told the publication: "The issue of succession is probably the single most delicate issue facing Italian companies, especially in the luxury and fashion sectors, where companies are tied very closely to the vision and genius of the founder."
He added that there is always a risk when fashion houses change hands that it may not be strong enough to keep going.
Luca went on to say that it was common for Italian men to believe "that they will live forever".
Recently, it was rumoured that Twilight actor Taylor Lautner could be the next face of Giorgio Armani.
The 17-year-old would be following in the footsteps of David Beckham, as he and Victoria have both featured in underwear ads for the brand.
