In a meeting lasting around 90 minutes, the Prime Minister updated her top team on the on-going discussions with the Unionists to secure an agreement propping up the Tory minority government.
Mrs May was attempting to thrash out a pact with Mrs Foster at a meeting in Downing Street to prevent the collapse of her administration.
Mrs Foster arrived with colleague Nigel Dodds and waved to reporters in Downing Street but refused to be drawn on whether she would agree to a deal on Tuesday.
A failure to gain support from the Northern Irish party would risk the Queen's Speech being voted down next week, and Jeremy Corbyn has said Labour will be pushing hard for that outcome.
Sinn Fein has warned such a move undermines power-sharing talks in Northern Ireland and the party's seven MPs have flown to London where they will hold a briefing with reporters.
Downing Street said Cabinet ministers had discussed the Government's legislative programme when they met earlier but refused to be drawn on discussions about plans to deal with the DUP.
"There was an update on the on-going talks with the DUP," the Prime Minister's official spokesman said.
As Mrs Foster met with her MPs in Westminster, she said: "The future's bright", prompting Ian Paisley junior to respond: "The future's orange".
The Tories and the DUP are considering a "confidence and supply" arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.
It comes after Mrs May told Tory MPs: "I'm the person who got us into this mess and I'm the one who will get us out of it."
Her most senior minister Damian Green has confirmed the Queen's Speech setting out the Government's programme could be delayed if a deal is not reached in time for it to go ahead on Monday as planned.
The PM told the backbench 1922 Committee on Monday a deal with the DUP would not affect power-sharing talks in Northern Ireland or LGBT rights.
Mrs Foster has also rejected suggestions that the mooted agreement could undermine a return to power-sharing arrangements at Stormont amid claims from political rivals the Government's stated impartiality as a mediator would be fatally undermined.
The DUP leader declined to give details of what she termed a "positive engagement with the Conservative Party".
Sinn Fein's Gerry Adams turned Mrs May's own slogan against her to brand it "a coalition of chaos", adding: "Any deal which undercuts in any way the process here or the Good Friday Agreement is one which has to be opposed."
It is thought Mrs Foster, despite being a Brexit supporter, could seek assurances from Mrs May that she will pursue a softer exit from the EU, given Northern Ireland's 56% Remain vote and the DUP's desire not to see a return to a hard border with Ireland.
The DUP leader is almost certain to ask for greater investment in Northern Ireland as the price of a deal.
Any demands on maintaining the pensions triple-lock and the universal winter fuel allowance could give Mrs May a convenient excuse to drop manifesto pledges which appeared to be deeply unpopular with voters.
Movement on security and legacy issues from the Troubles may prove more difficult for Mrs Foster to extract from the Government.
New Environment Secretary Michael Gove indicated the Government was ready to soften its approach to austerity, telling BBC Radio 4's Today programme "we also need to reflect on what the election result told us about the way that people want to see the economy managed in the future".
"We need to get on with the job of reducing the deficit so that we do not saddle the next generation with the burden of debt, and the larger the deficit the more money that should be spent on health and education is actually spent on paying down debt," he added.
Mr Gove said there was a need to ensure public spending was sustainable but stressed that "we also need to take account of legitimate public concerns about ensuring that we properly fund public services in the future".