Missoni, his wife, and a couple of their friends were last seen boarding a plane at a resort in the Los Roques archipelago off the coast of Venezuela, bound for Caracas, ABC News reported.
"A plane cannot vanish in this way, on a short route, without leaving any trace. I remain convinced that the least plausible reason is that they crashed into the water," Missoni's oldest son, Ottavio, told Italian newspaper Corriere Della Sera Wednesday.
Ottavio Missoni based his reasoning on a text message sent from the cellphone of Guido Forsti, who was on the plane, to Forsti's son more than 48 hours after the plane and its passengers disappeared.
The text said: "Call now. We are reachable."
Meanwhile, Italian Foreign Minister Giulio Terzi said Friday that the search for the Vittorio Missoni and the others will continue "until some conclusive indication is found," Italy's ANSA news agency reported.
Missoni is the chief executive officer of the Missoni fashion company famed for its zigzag-patterned knitwear.
More than 400 people in boats, planes and helicopters searched Wednesday for those missing without success, Venezuelan officials said.
2014: The Year in Music [PHOTOS]