French President Emmanuel Macron is expected to announce the proposed loan of the tapestry, which depicts the Norman Conquest of England, during a visit to Britain on Thursday, according to The Times.
The French presidency confirmed on Wednesday that it was in talks to loan the Bayeux Tapestry to Britain, but that the 11th-century embroidery would not be transferred before 2020.
An official in Macron's office said "it will not be before 2020 because it's an extremely fragile cultural treasure which will be subject to major restoration work before being transported anywhere."
And a spokesperson for the Ville de Bayeux told The Local that it could be even longer before tapestry makes it to British shores.
"We are in the process of planning a new museum which will house the embroidery. That means it's unlikely the loan will happen before 2023 when it is hoped we will be ready to close for the new development in France," she said.
The spokesperson suggested that Wednesday's announcement was a little premature, saying that there was a lot to be decided before the loan could go ahead.
"At the moment we need to remain calm over the situation because no one knows if it's possible to send the embroidery to the UK. We must first conduct analyses to see if it's capable of making the trip and there will be a lot of conditions before it goes ahead.
"That said, we are very open to working with heritage organisations in the UK and are already very linked with the British Museum," she added.
Preparations for the relocation are underway following months of discussions between cultural officials in both countries, The Times said.
However it could be five years before the tapestry -- which is nearly 70 metres (230 feet) long and 50 centimetre high -- actually arrives on British shores, the paper added.
No decision has been made about where it would be displayed during the loan, it said citing British officials.
The Bayeux tapestry, which dates from around 1077, depicts the story of William the Conqueror and the Battle of Hastings in 1066 and is displayed in Bayeux, in Normandy.
While it has rarely been moved, it was displayed in Paris in 1804, and again briefly at the Louvre in 1945.
In the past Britain has unsuccessfully tried to convince the French to lend them the tapestry, once in 1953 for the Queen's coronation and again in 1966 for th 900-year anniversary of the Battle of Hastings.
President Macron will hold talks with May at a Britain-France summit at Sandhurst, a British military academy, later this week, with co-operation on various issues set to be discussed.