The Tory Home Secretary has signalled her support for a Brussels initiative to return the migrants who have surged into mainland EU countries in recent months back to Africa.
She is understood to believe the move will help Britain by raising the possibility of migrant camps at Calais being cleared.
Mrs May is due to discuss the plan with other EU interior ministers at a meeting in Brussels today.
And it comes as David Cameron holds fresh talks with German Chancellor Angela Merkel today to discuss his plans for a new EU deal for Britain.
The secret EU plan was disclosed by the leak of a diplomatic document today.
“Increased return rates should act as a deterrent to irregular migration,” the document said.
“Member states must systematically issue return decisions, take all necessary steps to enforce them and provide adequate resources, necessary for identifying and returning illegally staying third-country nationals.”
Proposals in the document include detaining thousands of failed asylum seekers to stop them from absconding to avoid deportation.
Brussels will also threaten to withdraw aid, trade deals and visa arrangements from African countries refusing to take back economic migrants under the plan.
A special unit of the EU border agency Frontex is to be set up to oversee the deportations, according to the document.
It added: “While member states are primarily responsible for carrying out returns, the immediate creation of a dedicated return office within Frontex should enable it to scale-up its support to facilitate, organise and fund return operations.”
EU member nations that fail to enforce internationally agreed refugee rules by deporting “irregular migrants” would face legal action and fines from the European Commission, according to the document.
More than 400,000 asylum seekers who have entered the EU are expected to have their claims for refugee status rejected.
Some from Syria, Afghanistan and Libya are likely to be among those being deported if their asylum applications fail.
Britain is not part of the deportation plan because the country is not part of the border-check free Schengen zone.
But Mrs May believes that deporting failed asylum seekers from mainland Europe will also ease pressure on Britain’s borders.
In her speech to the Tory conference in Manchester earlier this week, she announced plans for deporting thousands more failed