The appeal to France came from an Italian historical society and has received support from Florence's provincial government, which announced the initative on its website and said it would seek to widen the campaign.
The precious painting was stolen from the Louvre in 1911 by an Italian who was arrested in 1913 after trying to sell it to an antiques dealer in Florence.
The Mona Lisa was briefly put on display in the Uffizi Gallery before being returned to France, where it has been since it was painted in the 16th century.
"This is not a declaration of war against France. It's an appeal aimed at collaboration," said Silvano Vinceti, the head of a historical society organising the improbable appeal together with the province of Florence.
"This would be an event of enormous cultural and historic value as well as a marvellous occasion for the whole of Italy," he said.
"The Gioconda has left the Louvre museum three times. It can do so again."
Vinceti said the aim was to collect 100,000 signatures within the next few months and to lobby the Italian parliament to back the campaign, which will appeal directly to the Louvre and to the French ministry of culture.
A spokesman for Florence's provincial government said: "We are supporting this. We will try and get more backing from city and regional authorities too."
The rivalry between Italy and France over ownership of the Mona Lisa is a saga spanning centuries and still stirs passions on both sides of the border.
Leonardo is believed to have started the work in Italy and finished it in France.
It is now jealously guarded by the Louvre and was last taken out of the famous Paris museum in 1974 when it was loaned to Tokyo in an exceptional move – the only time the painting has left the country since its theft.
Vinceti is leading a team of archaeologists digging up a former convent in the centre of Florence to try and find the remains of Lisa Gherardini, the woman believed to be the model for Leonardo Da Vinci's painting.