The tower, designed by British architect Richard Rogers, was completed in 1986 after an eight-year construction period.
Companies are rethinking their office space after the COVID-19 pandemic demonstrated that working from home was feasible.
The pandemic has also accelerated automation efforts, with Lloyd's, which insures complex risks ranging from oil rigs to football players' legs, increasingly shifting away from doing business on its underwriting floor.
"As we adapt to new structures and flexible ways of working, we are continuing to carefully consider the future requirements for the spaces and services our marketplace requires," an email from a spokesperson said.
"We, like many other organizations, are considering a variety of options for our workspace strategy and Lloyd's future leasing arrangements. We intend to reveal our plans in 2022."
Ping An, a Chinese insurer, purchased the building in 2013 for 260 million pounds ($353.91 million).
The lease is set to expire in 2031, but there is a break clause in place in 2026.
React, a real estate publication, broke the story first.
Lloyd's announced on Monday that chief operations officer Jennifer Rigby would be departing this week, with chief financial officer Burkhard Keese taking over her responsibilities for technology and operations.