The prime minister will meet union leaders later to talk about the next steps of her Brexit plan.
Theresa May will try to find compromise with Unison, the TUC, Unite and the GMB after her deal was overwhelmingly voted down by MPs last week.
But a number of the leaders have backed delaying the UK’s exit date from the EU and some support another referendum.
Meanwhile, Chancellor Philip Hammond will tell industry leaders that the UK “is a great place to do business”.
Giving a speech to the World Economic Forum in Davos, he will try to reassure businesses that Britain is “determined… to make sure it remains that way” after it leaves the EU.
It comes a day after Sony announced it was planning to move its European headquarters from the UK to the Netherlands to avoid disruptions caused by Brexit.
The UK is due to leave the EU at 23:00 GMT on 29 March.
Mrs May spoke to a number of union leaders ahead of the vote on her deal last Tuesday, hoping to drum up support – but it did not pay off, with MPs rejecting her proposals by 230 votes.
Since the defeat, she has been meeting leaders of opposition parties and factions within her own as she called for MPs to “work constructively together” to find a way forward.
Labour leader Jeremy Corbyn has refused to join the talks until Mrs May rules out the UK leaving the EU with no deal, which he says would bring “chaos” to the country.
However, the head of Unite Len McCluskey, who is a close ally of Mr Corbyn, will be among the union leaders she meets later.
What options for Brexit do the unions back?
The TUC’s Frances O’Grady, Unison leader Dave Prentis and the general secretary of the GMB, Tim Roache, have all publically backed extending Article 50 – the mechanism by which the UK leaves the EU – to postpone the exit date of 29 March.
All three have also said the government should give the public the final say, either through a referendum or general election.
But Mr McCluskey is against another referendum on the EU, writing in the New Statesman that it “risks tearing our society apart”.
On Wednesday, the PM met the first ministers of both Scotland and Wales on the future of her Brexit deal, but both said she seemed unwilling to compromise.
Scottish First Minister Nicola Sturgeon said there “wasn’t much indication that the prime minister is listening to, or hearing the concerns of people in Scotland”, while Welsh First Minister Mark Drakeford said she “repeated many of her red lines”.
How are MPs trying to move Brexit plans on?
The PM is hoping to tweak her deal to address concerns about the Northern Irish “backstop” among her own backbenchers and Northern Ireland’s Democratic Unionist Party, which she relies on to keep her in power, ahead of another vote on her proposed way forward next Tuesday.
The backstop is the “insurance policy” in the withdrawal deal, intended to ensure that whatever else happens, there will be no return to a visible border between Northern Ireland and the Irish Republic after the UK leaves the EU.
Both the UK and the EU believe that bringing back border checks could put the peace process at risk but critics say the backstop keeps Northern Ireland too closely aligned with the EU and separate from the rest of the UK – and that the UK would be permanently trapped in it.
However, a number of MPs are proposing amendments putting forward alternative plans to the PM’s deal with the EU – including seeking an extension to the UK’s exit date.
Labour MP Yvette Cooper has tabled one that would give time for a bill to suspend the Article 50 process for leaving the EU – enabling it to last until the end of the year – if a new deal has not been agreed with Brussels by the end of February.
Her Labour colleague, Rachel Reeves, has also tabled an amendment to extend Article 50.
BBC political correspondent Iain Watson said the pair met Mr Corbyn to discuss the proposals.
He said they recognised that, as Ms Cooper’s amendment would lead to a bill, it would be amendable – meaning the nine-month extension could be significantly reduced to reassure MPs nervous of the timeframe.
Ms Cooper’s amendment is also backed by several Remainer Conservatives and is the only amendment that would be legally binding on the government, if passed.
Other amendments would ask the government to consider a range of options over six full days in Parliament before the March deadline, to set up a “Citizens’ Assembly” to give the public more say or to insist on “an expiry date to the backstop”.