"They're mine," Johnny Weissmuller Jr. said, his voice weak from terminal cancer. His wife, Diane Weissmuller, said the champion swimmer -- who was also known for playing Tarzan in movies -- specified in his will that the medals be given to his son, the Miami Herald reported.
The hall's president, Bruce Wigo, won't release the items without seeing the will. The museum's collection includes five gold medals, one bronze medal, several photographs, a swimsuit from the 1928 Olympics and a Tarzan loin cloth.
"It was always a verbal agreement with Johnny," Wigo said.
In 2004, several items were stolen from the hall, including Weissmuller's memorabilia, when a janitor swapped imitations for the real items. Police arrested the janitor and restored the items in September 2005.
"We don't feel the items are secure," Diane Weissmuller said.
"How do you put a price on a Weissmuller gold medal?" Weissmuller Jr. said. "You can't. It's priceless and irreplaceable."