The small aircraft transporting the 58 year old co-owner of his family's famed Missoni label, his wife and four others vanished shortly after take-off from the resort of Los Roques.
Venezuelan air and sea rescue search operations have so far proved fruitless, but Missoni's sister and brand co-owner, Angela, insists his relatives are still praying for his safe return.
A statement issued by Angela Missoni to E! News reads: "My children and nephews are with my parents, all together at this difficult time. We are all moved by the affection and help we've had so far from the whole world and thankful to the authorities for their tireless search and rescue efforts.
"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 possible avenues.
"Our deepest thanks go to the multitude of supporters that have reached out to us from all over the world, and we ask that you join us in the hope that the Missoni, Scalvenzi, and Foresti families will soon be reunited. We are full of hope and trust the great work the Authorities have been doing so far. We will not give up."
The fashion mogul is thought to have been returning from a holiday with his wife and two friends, Italian businessman Guido Foresti and his wife Elda Scalvenzi, when the aircraft went missing.
It's the second plane disappearance in South America in as many months - Latin singer Jenni Rivera was feared dead after her plane vanished shortly after taking off from Mexico on 9 December (12). The wreckage of the aircraft was later found nearby, and all seven people onboard were declared dead.