The British government is trying to find a way to protect some 4,500 jobs in Belfast endangered by a trade dispute.
Bombardier is Northern Ireland's largest manufacturing employer and May's Conservatives are dependent on the support of the small Northern Irish Democratic Unionist Party (DUP) for their majority in parliament.
But earlier this year Boeing alleged that Bombardier's CSeries programme had benefitted from government subsidies - both from Canada and the United Kingdom - that has effectively enabled Bombardier Aerospace to sell the CSeries at below its production costs - creating an unfair advantage for the Canadian group.
U.S. President Donald Trump (R) speaks to Britain's Prime Minister Theresa May during in a working dinner meeting at the North Atlantic Treaty Organisation headquarters during a North Atlantic Treaty Organisation summit of heads of state and government in Brussels, Belgium, May 25, 2017.
A US ruling against Bombardier this month over punitive tariffs for the aircrafts would be devastating news for the Belfast plant, where some 4,500 people are employed.
The Canadian group has previously said that it hopes the C-Series could generate more than 800 jobs for Northern Ireland once the programme reaches peak production.
The Times of London first reported the phone call.
They said that ministers across the government have communicated with Boeing, Bombardier and the USA and Canadian governments.
A government spokesperson said it was working to safeguard Bombardier's operations and its workers in Belfast.
The British government said in a statement that Britain's priority is to encourage Boeing to drop the case in favor of a negotiated settlement.
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A Boeing spokesman said on Tuesday the company would not comment on a meeting between heads of state.
Bombardier could be hit with punitive tariffs, making any future United States customers for the C Series jets hard to find.
But the DUP is certain to maintain its pressure on her.
Bombardier makes the CSeries CS100 and CS300 state-of-the-art carbon wings at a plant in Belfast, along with other aircraft components.
Northern Ireland now does not have its own functioning government.
"We're not there yet, and the work still has to continue".
Boeing said: "This is the normal course of action for addressing instances where a competitor is selling into the U.S. market below cost and we will let the process play out".
Bombardier condemned Boeing's position as "an unfounded assault on airlines, the travelling public and further innovation in aerospace".
Free trade creates wealth and employment.
Industry sources said Boeing was unlikely to back down in the case, which mirrors a wider row with Europe's Airbus over subsidies that it perceives as a strategic threat.