The group was in a small plane carrying six people that plunged into the sea shortly after taking off from the Los Roques islands in January.
The wreckage was found in June at a depth of 230ft.
Rescue teams have been carrying out searches in the area for several days.
Venezuelan Attorney General Luisa Ortega issued a statement saying that she was going to meet relatives arriving in Caracas to update them on the rescue mission.
El Universal newspaper, Italian media and news agencies reported on Thursday that the bodies of the four passengers and the co-pilot, Juan Carlos Ferrer, had been found.
They are still looking for the remains of the Venezuelan pilot, German Marchant, according to those reports.
But El Universal has now said that rescue teams working north of Los Roques have not yet retrieved the bodies.
Vittorio Missoni and his partner, Maurizia Castiglioni died in the crash alongside two Italian friends who were holidaying with them in the Venezuelan archipelago, Guido Foresti and Elda Scalvenzi.
The twin-engine aircraft disappeared on 4 January.
Vittorio Missoni was the son of the late founder of the Italian Missoni fashion house, Ottavio Missoni, and co-owned the firm with his siblings.
A piece of luggage from the aircraft was found off the Dutch island of Curacao, about 200 miles west of Los Roques, later that month.
Los Roques, an archipelago made up of dozens of islands some 95 miles off Venezuela’s coast, is one of the area’s most popular holiday destinations.
At least 158 people have died in Spain's worst flooding disaster in generations. On October…
Google has been fined two undecillion (a two followed by 36 zeroes) roubles by a…
Embarking on a home remodel is an exciting journey, promising enhanced comfort, increased property value,…
The US presidential candidates continued to campaign across key swing states on October 20. Footage…
Elon Musk has said he will give away $1 million a day to a registered…
India and Canada have decided to expel their top envoys along with other diplomats as…