Lloyd's is in talks to move out of the revolutionary 1986 building due to "frustrations" with its design, the newspaper reports (£).
"Lloyds has made no secret of its frustrations with its headquarters, which has lifts and services outside the building," the newspaper says. "Because of advances in technology Lloyd's now uses only three quarters of the 350,000 square foot site, subletting the spare space".
According to the paper, Lloyd's former chief executive Richard Ward said last year: "There is a fundamental problem with this building. Everything is exposed to the elements, and that makes it very costly."
The insurer favours relocating to nearby 40 Leadenhall Street, an as-yet unbuilt tower designed by Make Architects and dubbed "Gotham City," the paper adds.
The Lloyd's was awarded Grade 1-listed status - the highest level of protection available to a building in England - in 2011. It was Rogers' second major building, following the completion of the Pompidou Centre in 1977, which he co-designed with Renzo Piano.
The building achieved instant fame for the way its stainless steel services and circulation are mounted on the outside of the building's concrete structure, creating open, flexible interior spaces.
"We were able to convince Lloyd’s that we would put the mechanical services on the outside because mechanical services have a short life," Rogers told Dezeen in an exclusive interview last year.
"[We] kept the floors clear because Lloyd’s said they wanted two things," Rogers added. "They wanted a building that would last into the next century - we met that one - and they wanted a building that could meet their changing needs."
Lloyd's became one of the most recognised example of the "high-tech" style of architecture, although Rogers himself said he was never keen on the term.
"I have no great love for high-tech," he said. "One would like to think one uses the appropriate materials, but of course appropriate materials are shaped by the time you live in."
"We thought Lloyd's was the absolute ultimate in the art of technology," he added. "When I look at it now, it's practically hand made."
Update: in a letter to the Sunday Times newspaper, Rogers said that a Lloyd's spokesperson had told the architect that the company had "neither intention of leaving – they are, in fact, negotiating their rent review with the building’s new owners – nor are they unhappy with the way the building performs."
"The building has proved to be very flexible and is still a highly desirable office that has attained some of the best rents in the city and proved to be a fantastic commercial success," said Rogers. "And we know that it will remain so."
The interview with Richard Rogers features in our new book, Dezeen Book of Interviews, which is on sale now.