"We are still in negotiations, and on that basis we don't know when and if this will conclude", a spokesman said, adding that a much-rumoured Cabinet meeting to allow ministers to sign off the deal had not been scheduled.
"Repeatedly people seem to make the same mistake over and over again, assuming that if the British cabinet agrees something, well, then that's it then, everything is agreed".
Brexiters are adamant that there must be a mechanism that would allow the United Kingdom to leave, and many back one that would allow the United Kingdom to withdraw unilaterally - without Brussels' consent - which has been rejected by figures such as the Irish Prime Minister, Leo Varadkar.
The question of how to avoid a "hard border" between Northern Ireland and the Irish Republic after Brexit has proved to be the toughest issue in the exit talks.
International Trade Secretary Liam Fox sent a message to the prime minister that quitting a backstop arrangement, aimed at preventing a hard Irish border, should be a decision for the United Kingdom alone.
Former Brexit secretary David Davis said the full government legal advice on Brexit must be published and insisted how the United Kingdom could exit from the customs union must be "pinned down" before MPs and peers vote on the deal.
Leaving without an agreement would mean some "hiccups in the first year", but the United Kingdom would have "all the rights and controls over our own destiny", he added. In a phone call with May on Monday, Irish Prime Minister Leo Varadkar said he would consider a "review mechanism" for the backstop.
But he appeared to urge Mrs May to make available the full legal assessment of Attorney General Geoffrey Cox QC to her cabinet.
May's plan would see the whole United Kingdom effectively agree to remain in the customs union to help avoid a hard border with Ireland as a backstop if no other arrangement can be found.
A potential sticking point could be demands for European Union fishing fleets to be given continued access to British coastal waters as the price for agreeing to Mrs May's UK-wide backstop, the Daily Telegraph reported.
Later, addressing leaders of the European People's Party group, Barnier warned of the threat that rising nationalism and populism pose to the EU ahead of European Parliament elections in May.