A small plane carrying four Italian tourists, including Vittorio Misson, the head of the Missoni fashion business, disappeared off the coast of Venezuela on Friday.
A sea and air search began Saturday and is still underway.
As the search for the aircraft carrying Vittorio Missoni, his wife Maurizia Castiglioni and two others continues, family members are "exploring other possibilities."
Angela Missoni, Vittorio Missoni’s sister and the chief designer of the Missoni label, issued a statement saying that the family had not given up hope.
The small plane disappeared after takeoff from the island resort of Los Roques.
“I am in direct touch with the Italian Foreign Ministry and now in Rome to meet people and the Police of State to report the disappearance of my brother," she said.
"[We are] coordinating information and offers of aid we’ve received from all over the world. My brother Luca is in Venezuela being an active part of the search."
"He’s a pilot and now also involved in the flight over the area.”
“At this time, we have no further specifics regarding these efforts except to say we are confident they will continue at the same pace and that the search will explore all avenues.”
Several Italian news outlets reported speculation among Missoni’s siblings that the fashion executive might have actually been the victim of a kidnapping.
However, a Reuters report cited the comments in La Stampa of another pilot who said he had seen the small plane disappear into a large cumulus cloud.
The Missoni family is widely revered in the fashion industry for its kaleidoscopic patterns applied to sweaters, home furnishings, beach towels and even water bottles.