Lloyd's will put the proposed destination to its members and then look for regulatory clearance for the subsidiary, which will be used for EU business, chairman John Nelson told the Financial Times.
With 11% of its revenue coming from the EU, the market had to act quickly, Nelson told the newspaper.
"Insurance is a mobile business. In common with other financial institutions, we need to put our plans in place, at least on a precautionary basis," he said.
The subsidiary is likely to cost tens of millions of pounds to Lloyd's members due to high compliance and regulation costs and the market will change its plans if a deal between the UK and EU allows it to trade from London, Nelson told the Financial Times.
Lloyd's is lobbying strongly for a continuation of the current passporting regime. Passporting arrangements enable firms based in one EU member state to trade anywhere in the bloc without having to seek multiple authorisations.
The UK's financial services industry has made it clear that its preferred option as part of the Brexit process would be for the UK to seek access to the single market, and to continue to benefit from passporting rights.
However, numerous reports have suggested that this type of single market access would almost certainly require the UK to agree to freedom of movement of EU workers, and to comply with relevant EU regulations. Some financial contribution to the EU is also likely to be required, as is currently the case for the non-EU countries that form part of the European Economic Area (EEA), including Norway.