Boris Johnson will be left with nothing to take back to MPs on Saturday if he does not meet EU demands by midnight tonight, Michel Barnier has indicated.

The EU's chief negotiator told EU27 ministers at a closed meeting on Tuesday that a new Brexit agreement needed to be place by the end of Tuesday for it to be considered at an EU summit later this week.

Mr Johnson is counting on having a deal in place for Thursday's meeting in Brussels so he can have it ready when it faces MPs the next day in parliament for an emergency Saturday sitting.

Diplomats say Mr Barnier told ministers that UK proposals so far are not good enough, despite reports that UK presented yet another new legal text in talks on Monday.

"As part of the talks process, there is of course back and forth and new texts have been shared by both sides repeatedly - that's what a negotiation is," a UK government spokesperson said on Tuesday morning.

Going into the Luxembourg meeting with ministers, Mr Barnier struck an up-beat tone, telling reporters: "Even if agreement will be difficult – more and more difficult, to be frank – it is still possible this week."

He added that that "work has been intense all through the weekend and yesterday". Talks ran on until midnight on Monday, having entered a so-called "tunnel" of intensified negotiations on Friday.

Diplomats say the chief negotiator did not go into extensive detail about discussions with the UK. Talks are focusing on the issue of customs processes across the Irish border, a key sticking point.

Brexit Secretary Steve Barclay, who was also in Luxembourg and who spoke with Mr Barnier at the margins, told reporters: "The talks are ongoing, we need to give them space to proceed but details conversations are underway and a deal is still very possible.”

If no deal is struck in time for this week's summit, UK law will force Mr Johnson to delay Brexit yet again, breaking one of his key campaign pledges and opening him up to criticism from Brexiteers. Under the so-called Benn Act, the prime minister must request and accept an extension if no deal is in place by the 19 October – when MPs will come to Westminster for their emergency Saturday sitting.

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The failure to sign an agreement at the summit would likely mean that talks would continue into the next week. Irish deputy prime minister Simon Coveney told reporters in Luxembourg:

"I don’t want to raise expectations about later on today or this evening, but if there is going to be the positive report that is needed to EU capitals tomorrow in advance of the EU summit, then clearly a big step forward is needed today.

"It is of course possible to move beyond the summit and continue talks next week. That is feasible because the UK isn’t due to leave the EU until the end of the month.

"From everybody’s perspective, if we could provide clarity at this leaders summit, that would be a welcome development."

For some EU leaders, however, it was already too late to get a deal for the meeting. Speaking on Monday Finnish prime minister and holder of the rotating EU presidency Antti Rinne told reporters: “I think there is no time in a practical or legal way to find an agreement before the EU Council meeting. We need more time.”

Even if agreement will be difficult – more and more difficult, to be frank – it is still possible this week. Michel Barnier

Spanish foreign minister Josep Borrell, who is set to take over as the EU’s foreign affairs chief, meanwhile said there might be a need to “stop the watch” and ask for more time.

Boris Johnson spoke about the progress of Brexit negotiations with French president Emmanuel Macron in a 20-minute phone call this morning which Downing Street described as “constructive”.

The PM’s official spokesman also confirmed that Mr Johnson met with representatives of the DUP in Number 10 on Monday evening, but declined to go into details of the discussions.

Asked whether the UK recognised Michel Barnier’s midnight deadline for a deal to be agreed, the PM’s spokesman said: “The prime minister is aware of the time constraints we are under. We want to make progress toward securing as soon as possible and we want to make progress ahead of the European Council on Thursday.”

Boris Johnson will have to face MPs on Saturday after the summit (EPA)

Asked whether Mr Johnson would accept a technical delay to Brexit to finalise details once a deal had been agreed in outline, the spokesman said: “The PM has said on many occasions that we need to leave on 31 October.”

He confirmed that MPs would have to approve the political declaration on future EU/UK relations as well as the withdrawal agreement in order for a deal to be completed. He said that discussions have been taking place on the declaration - which covers issues like the ultimate trading relationship between the UK and EU – but declined to go into details of Britain’s proposals.