The note, written to Jackie's sister-in-law Ethel, following Robert Kennedy's assassination in 1968, has been sold for up to $25,000 in the past. Now, there are suggestions that the note may have been stolen from the Kennedy family's possession decades ago.
In 2006 its US owner Richard Goodkin put the two-page letter up for sale at Heritage Auctions with a $15,000 starting price.
It was at that point that Max Kennedy, the son of Robert, put a halt to the sale, claiming that the note had been illegally taken from his parents' home in McLean, Virginia.
A US district judge will now decide who will be granted ownership of the letter, which currently resides with the FBI.
No criminal charges will be brought, the FBI has concluded.
The letter details Jacqui's concern for the couple's two children following Robert's assassination while campaigning for the presidential election.
In 2009, the son of a plumber who had once been employed at the Kennedy residence sold the document to a Connecticut dealer for $6,000.
Former US attorney Richard Roper told US television channel News 8: "She [Ethel] could definitely say: 'If I were to give that letter to anybody, I wouldn't give it to a plumber working on my house.'"