Chairman John Nelson told City A.M. he was "hopeful" the UK could strike a deal with the rest of the EU to preserve the financial services passport, which lets firms do business across the other 27 members from a UK headquarters. However, he added: "We have to plan on a contingency basis, so that's what we're doing.
"We've had some contingency plans in place for a while. We're refining them at the moment ... We have to have our plans ready to roll in the fairly near future."
Chief executive Inga Beale told the BBC the plans could include setting up an EU subsidiary or Lloyd's branches in continental Europe.
Read more: What does Brexit mean for insurance?
Nelson has previously said Lloyd's would be forced to move operations away from London if the UK and EU did not reach a decent agreement over financial services. He indicated today that Lloyd's would not wait for the Prime Minister to trigger Article 50 or for the shape of the negotiations to become clear before starting to get those ducks in a row.
Publication of the kind of back-up plans Lloyd's is considering will come "in the next few months", Nelson told City A.M.
"We're busy making the case for the maintenance of passporting rights," he said. "The full impact of the loss of passporting rights... could be quite substantial. People are beginning to see that.
"The second thing is there is great pressure from third party countries such as Japan, the US and China on the UK government to preserve passporting rights in terms of maintaining their investments here.
"And the other thing which people are beginning to discuss is the issue of the EU itself. If you look at the financial services institutions in the EU I think many are as keen as we are to preserve passporting."
Read more: What now? The UK and the Single Market
The comments come in a week where the debate over passporting has taken centre-stage in the City, following the publication of official statistics which showed 13,000 firms operating in the UK made use of the scheme and ratings agency Moody's saying British banks could survive operating without the rights.
Nelson would not be drawn on whether Lloyd's had been contacted by governments or officials in other financial hubs such as Frankfurt or Amsterdam about the possibility of a relocation.
The company, which reported its half-year results this morning, also said the squeeze on margins in the insurance industry was the worst it had been for "many, many years". Its combined ratio, which measures underwriting profits, climbed from 89.5 per cent to 98 per cent, where a ratio above 100 per cent indicate losses.