The British-flagged Bayesian, a 56-metre-long (184-foot) luxury sail boat carrying 22 passengers and crew, was anchored off the port of Porticello, near Palermo, when it capsized and rapidly sank after being struck by a pre-dawn storm on Monday.
The source did not identify the body as belonging to 18-year-old Hannah Lynch, but she was the only person still unaccounted for. Italian news agency Adnkronos said she was found inside the yacht.
The wreck is lying at a depth of 50 metres and once inside the passageways are narrow. The fire brigade on Friday described rescue operations as "long and delicate", and said they involved more than 400 people, including 28 specialist divers.
The bodies of the other five dead passengers, including Lynch, were recovered on Wednesday and Thursday from inside the yacht. The body of the only crew member who died, onboard chef Recaldo Thomas, was found near the wreck on Monday.
Official identification of the corpses and autopsies are expected to begin after the transfer of the last recovered body to a hospital morgue in Palermo.
A judicial investigation has been opened into the sinking, which has baffled naval marine experts who say a boat like the Bayesian, built by Italian high-end yacht manufacturer Perini, should have withstood the storm.
The yacht's captain James Cutfield, his eight surviving crew members and passengers have been questioned by police, but have not made public comments. Investigating prosecutors are due to hold a press conference on Saturday.
COMPLEX SALVAGE OPERATION
Giovanni Costantino, CEO of The Italian Sea Group TISGR.MI, which owns Perini, told Reuters the shipwreck was the result of a string of "indescribable, unreasonable errors" made by the crew, and ruled out any design or construction failings.
Pulling the wreck out of the sea, where it is now lying on its right side, apparently intact, may help investigators determine what happened, but the operation is likely to be complex and costly.
Nick Sloane, a South African engineer who led the operation to salvage the Costa Concordia cruise liner that sank in 2012, said in Italian media interviews on Friday that the operation would cost up to 15 million euros ($16.7 million).
He told daily La Repubblica thatsalvaging the yacht would take six to eight weeks, including preparation work, and would have to be completed by mid-October, without specifying the reasons for the timing.
Bringing the yacht to the surface will have to be done "very, very slowly", and might take a couple of days, he said.
