The automaker told the prime minister during a private call with business leaders that it is preparing alternative sites abroad, the report said.
In a statement to Reuters, Ford said a no-deal Brexit would be catastrophic for its manufacturing operations in Britain.
"We will take whatever action is necessary to preserve the competitiveness of our European business."
Ford, which operates two engine plants in Britain, last month said that it faces a bill of up to $1 billion if Britain leaves the European Union without a deal.
Car makers and other manufacturers have warned of the cost of a no-deal Brexit, including higher tariffs, disruption to supply chains and threats to jobs. Britain is scheduled to leave the EU on March 29.
Other companies have delivered the same warning as Ford, The Times reported, citing another participant on the private call with May.
"This isn't about contingencies any more - we are taking steps because of the uncertainty. It's real," the report quoted the participant as saying.
Last week Nissan Motor Co said it scrapped plans to build its new X-Trail SUV in Britain and will produce it solely in Japan, saying that uncertainty related to Brexit was making it hard for it to plan for the future.
Ford is a top-selling automotive brand in Britain, which is its third-largest market and the destination for roughly one in three cars made at its plant in Cologne, Germany. It employs about 13,000 people in Britain.
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