Mrs May assured ministers that there would be another Cabinet before any agreement is settled, though her official spokesman said no extra meeting has yet been scheduled ahead of the regular weekly gathering next Tuesday.
With a Brexit deal nearing completion with Brussels, the PM is trying to secure the agreement of her cabinet to press on with finalising the terms for Brexit.
Mrs May's warning to the Cabinet will be seen as a plea to pro-Leave ministers to give any deal a fair wind even if it involves further compromises.
The Conservative MP said that Tony Blair's failure to publish his own government's legal advice from its then attorney-general on the Iraq war meant that the Labour prime minister's reputation "never recovered".
There is a growing confidence in Whitehall the European Union will accept an all-UK backstop, which would mean the whole of Britain remaining in a customs arrangement with Brussels to avoid a hard Border if a trade deal can not be finalised by December 2020.
"For now, we are still negotiating and I am not, as I am speaking to you this morning, able to tell you that we are close to reaching an agreement", he told Belgian broadcaster RTBF.
There are significant outstanding issues in Brexit negotiations over the Irish backstop and work is ongoing to resolve them, British Prime Minister Theresa May's spokesman said on Monday.
The DUP is opposed to a Northern Ireland-specific backstop, since, if it came into effect, it would require Northern Ireland to be more closely aligned with the EU's customs and trade rules than the rest of the UK.More news: Steelers' game at Jacksonville flexed; four others protected
The threat of losing DUP support is a constant worry for Theresa May, without the Ulster unionists' support the Tories would be unable to guarantee a majority in parliament threatening any potential Brexit deal. But that goal has been complicated by May's intention to take Britain out of the EU customs union and single market.
Both sides agree there must be no customs posts or other barriers that could disrupt businesses and residents or undermine Northern Ireland's peace.
"We hope a deal can be done but we're not there yet".
A no-deal outcome, he said, "will have serious consequences for economy of Irish Republic". Neither the region's political leaders nor the Irish and British governments seem in a position to restore them.
"Looks like we're heading for no deal", Jeffrey Donaldson, one of 10 Democratic Unionist Party (DUP) lawmakers whose support May now needs to get any deal passed in the British parliament, said on Twitter.
The meeting will also be updated by Dominic Raab, the Brexit Secretary, on the latest preparations for a no-deal withdrawal from the bloc.
Meanwhile she was said to be on course to approve an economic partnership with the European Union which could develop into a Canada-style free trade arrangement.