The portrait, which was believed to have been either lost or never even painted, belongs to an Italian family which kept it in the vault of a Swiss bank, the Sette magazine reported.
It measures 61 by 46.5 centimetres (24 by 18 inches) and depicts the prominent Italian marquess, who was a patron of the arts, in profile.
It is "a faithful transposition of the famous sketch hanging in the Louvre," said Sette, which belongs to the Corriere della Sera daily.
"This is a sensational discovery although it is still short of confirmations," it said.
It quoted Carlo Pedretti, a world expert in the Tuscan painter (1452-1519), saying: "I can immediately recognize Da Vinci's handiwork, particularly in the woman's face."
Only around 15 works have been reliably attributed to Leonardo, including the "Mona Lisa" — the most famous and popular painting in the world.