Ford has said a no-deal Brexit would be catastrophic for the firm's manufacturing operations in the United Kingdom and that it would do "whatever is necessary" to protect its business.
Another participant on the private call with May said that other companies delivered the same warning as Ford, The Times reported.
Ford has become the latest carmaker to sound the alarm over Brexit, saying that it is stepping up preparations to move production out of Britain. "This isn't about contingencies any more - we are taking steps because of the uncertainty".
Labour MP Owen Smith said on Twitter, "After Nissan, Ford has now told Theresa May it is preparing alternative production sites - outside the UK".
Ford employs 13,000 people in the United Kingdom at sites in Bridgend, Dagenham, Halewood and Dunton.
Last week, Nissan Motor Co said it had scrapped plans to build its new X-Trail SUV in Britain and will produce it exclusively in Japan, adding that uncertainty over Britain's departure from the European Union was making it hard for it to plan for the future.
May's conference call with business leaders came after she told parliament on Tuesday she needed more time to negotiate a revised Brexit deal.
In January, Jaguar Land Rover, the UK's biggest carmaker, said it would cut 4,500 jobs in the United Kingdom, citing geopolitical issues, regulatory disruptions, and Brexit uncertainty.
In addition to Brexit worries, the vehicle industry faces a slump in sales of diesel cars and a slowdown in China.
Ford said last month that a no-deal Brexit will face a bill of up to £775m, the auto manufacturer operates two engine plants in the United Kingdom, placing up to 13,000 jobs at risk. "How many vehicle companies have to sound the alarm over Brexit before the Prime Minister listens?"