Joan Langbord and her sons say they found the 1933 gold "double eagles" years after the 1990 death of her father, Philadelphia jeweler Israel Switt.
U.S. Treasury officials say the 10 coins were stolen from the U.S. Mint, so the family has no legal claim to them.
Nearly a half million of the $20 double eagles were struck in 1933, but then melted into gold bars when the country went off the gold standard. A few mysteriously survived.
The Secret Service has long believed Switt and a cashier at the Mint were involved in the breach.
One double eagle sold for $7.59 million in 2002.