The French paper Le Monde reports that the treatment, an extract of fermented Asian papayas, was suggested by a French doctor, who met the 82-year-old Pontiff in June.
Dr Luc Montagnier actually met the Pope to try to persuade him to relax the Catholic Church's stance on the use of condoms as a way to tackle Aids in the developing world.
However, Dr Montagnier, who co-discovered the Aids virus, also used the meeting to propose the papaya treatment for the Pope, whose symptoms include a hand tremor and slurred speech.
Tissue damage
Dr Montagnier believes Parkinson's is linked to the damage caused to the body's tissues by molecules called free radicals that are released when cells convert oxygen into energy.
The theory is that the papaya extract contains chemicals that mop up free radicals, so that tissue damage is minimised.
Vatican officials, who have never confirmed that the Pope is suffering from Parkinson's disease, have not responded to the report.
Commentators have noticed an improvement in the Pope's healthon recent trips to Canada and Poland.
Dr Montagnier was director of a Paris laboratory that identified the virus that causes AIDS in 1983.
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