Lloyd's is expected to reduce its capacity by 10%-20% over the next two to three years, according to market sources.
The drop in capacity, from its present £14.9bn, could lead to smaller syndicates and managing agents drastically reducing their business.
Market sources said softening rates in certain lines of business, such as aviation, motor, commercial property and energy, were fuelling the debate.
One insider said: "The franchise board would want to keep downward pressure on capacity during the soft market rather than risking exposure to the central fund."
But other market observers said that Lloyd's made it clear in its results this month that rates were flattening in energy and aviation.
"It's too early to say whether Lloyd's will reduce capacity. It won't know until November what the figures will be for next year," they said.
"Lloyd's cannot dictate the amount of capacity in the market or in a specific class of business. That would go against competition rules."
Another source said: "What's more likely to happen, is that there will be a lot of noise about self discipline and the avoidance of writing uneconomical lines of business."
One Lloyd's underwriter said: "I don't know how Lloyd's could go about enforcing a reduction without sending out the wrong signals. It's after all not something rating agencies want to hear."
