The engraving carved by Italian artist Marcantonio Raimondi in 1505 shows da Vinci playing a lira da braccio - a European bowed string instrument of the Renaissance.
If verified, the engraving could be one of only three known depictions of the artist created while he was alive.
The engraving has belonged to the Cleveland Museum of Art since the 1930s, but the figure has long thought to be of Orpheus, a musician in Greek mythology, LiveScience reported.
He said that while Orpheus is usually depicted as a clean-shaven youth, the musician in the drawing is in his "late middle age, with a beard and centrally parted hair with long curls".
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Duffin compares the engraving with a portrait of da Vinci drawn by Francesco Melzi, "who joined the 54-year-old Leonardo's household as an assistant in 1506 and eventually became his principal heir."
"Melzi's portrait shows a man with a beard and long curls, and the very slight bump in his nose and the ridge above the brow are an excellent match for the long-haired, bearded [man] in the Marcantonio engraving," he said.
Some experts seem to agree with Duffin's idea about the engraving being that of da Vinci.
"This is serious and stands some chance of being right," said Martin Kemp, a professor emeritus of art history at Oxford University.
However, when and how Marcantonio met da Vinci remains a mystery, Kemp said.
He said Marcantonio was working in Bologna at this early stage of his career, and there is no obvious way they would have met.
"At this stage, I would say that it is temptingly possible but unproven," Kemp added.