A German tourist found the piece of luggage Jan. 10 on the island of Curacao, Women's Wear Daily reported Monday.
The Italian newspaper Corriere della Sera reported the bag belonged to Italian tourist Giorgio Neri and was placed on Missoni's plane Jan. 4 because there wasn't enough room on the plane he was taking from Los Roques, Venezuela, to Caracas.
The bag was empty when the German tourist found it but still had Neri's contact information. The German contacted Neri by email once he returned to Germany and Neri alerted the Missoni family, Corriere della Sera said.
The Missoni spokeswoman said the family was aware the bag had been found, Women's Wear Daily said.
"They are not drawing any conclusion. This is simply another piece of an already complex puzzle," the spokeswoman said.
Discovery of the bag on Curacao, about 124 miles from Los Roques, gave authorities a possible reference point for where Missoni's plane ma have gone down.
Missoni, his wife and a couple of their friends were last seen boarding the plane at a resort in Los Roques off the coast of Venezuela, also bound for Caracas.
Missoni is the chief executive officer of the Missoni fashion company famed for its zigzag-patterned knitwear.