The DUP are seeking further legal assurances about the deal, which has been decisively rejected by MPs twice, BBC reported.
The PM has received a boost after Esther McVey, who quit the cabinet over Brexit policy last year, signaled she could vote for the deal next week.
She said the prospect of a long Brexit delay called for "different thinking."
MPs voted on Thursday to ask the EU to push the date of Brexit back from 29 March to 30 June if the Commons approves a deal by next Wednesday – allowing time for legislation to go through.
However, if a deal is not agreed by then, EU leaders are contemplating a much longer delay.
European Council President Donald Tusk said EU leaders could be open to a long extension "if the UK finds it necessary to rethink its Brexit strategy."
What happened this week?
A series of Brexit votes have taken place in the Commons:
On Tuesday, MPs rejected May's withdrawal agreement for a second time by 149 votes
On Wednesday, MPs voted to reject the idea of the UK leaving the EU without a deal under any circumstances
Then, on Thursday, the Commons voted by 413 to 202 to seek an extension to Article 50 – the legal mechanism by which the UK is due to leave the EU
However, as things stand, the law has not been changed, as Wednesday and Thursday's votes were not legally binding.
That means the UK is still set to leave on 29 March - with or without a deal.
What are the UK's options?
While legally, there does not have to be a delay, politically it might be hard for May to avoid.
Thursday's motion saw Parliament agree to two options for a delay:
If MPs support May's deal next week – before a summit of EU leaders in Brussels on 21 March – then she will ask the EU for an extension of no later than 30 June
But if they don't support her deal for a third time, there could be a much longer delay and the UK may have to take part in elections for the European Parliament in May
Any delay will require the agreement of all other 27 EU members and talks about possible conditions could take place before the summit.
What has the government said?
Lidington, who is regarded as May's de facto deputy, told the BBC that, although the risk of the UK leaving without a deal had "diminished" as a result of this week's votes, it could still happen unless an alternative solution was found.
He urged MPs to "reflect" over the weekend on the deal on the table, which he said had the "great virtue" of having the backing of all 27 other EU governments and, most likely, the European Parliament too.
"I think there is some real impatience among the British public, and frankly among other EU governments, with this inability to agree in Westminster on the way forward," he told BBC Radio 4's Today programme.
"The alternative, spelt out very clearly and accepted by the House of Commons, is that you don't just have a short technical extension to our membership. You almost certainly need a significantly longer one."
EU politicians breathe deep, shuddering sighs at the thought of prolonging the cross-Channel agony of the Brexit process.
So will they or won't they agree to an extension? What conditions could they demand and how long would Brexit be delayed by?
Like so many things to do with Brexit – the answer is: We're not 100% certain.
Earlier this week, a number of EU leaders including France's Emmanuel Macron, Mark Rutte of the Netherlands and Spain's Pedro Sanchez sounded pretty hardline.
They wouldn't agree to delay Brexit, they said, unless the prime minister came up with a very good reason.
EU leaders are frustrated, irritated and fatigued by the Brexit process but it's also worth bearing in mind that they have two specific audiences in mind these days when they take to the cameras.