However Mr Davis said Mrs May would find it far trickier to get any deal similar to her Chequers plan through the House of Commons.
Yesterday he said “terror will win” in the Brexit negotiations and Britain would succumb to the “irrational fear” of a “no deal” divorce.
But he has now made clear he believes any agreement based on Mrs May’s unpopular Chequers proposals will still not get past MP’s when the hold their “meaningful vote” in the Commons.
Mr Davies tweeted today: “For the avoidance of doubt I believe the PM will get a deal with the EU but anything based on the Chequers plan or one that keeps us in the Customs Union will not pass the Commons. Time to revert to free trade deal suggested by EU?”
Negotiations are due to begin again in earnest after MPs vote on the budget later this week.
A summit of EU leaders in December is seen by Brussels as the last practical point for a Brexit deal to be agreed.
Mr Davis, speaking at an event at the Institute of Economic Affairs attended by key MPs from the DUP, was asked for his predictions on the Brexit process.
He said: “Terror will win.
“The fear of no deal, I think – we haven’t had a chance to talk about it much – but I think that’s an irrational fear of no deal or a World Trade Organisation deal.
“That will win and there will be a deal.
“It may take a few passes, there maybe a deal passes in Brussels and fails in Westminster.”
Mr Davis’s comments came after former Foreign Secretary Boris Johnson, who also walked out of the Cabinet over Chequer, described Mrs May’s plans as a “betrayal of Britain”.
Mr Johnson said the UK was “losing control” and urged the Prime Minister to “chuck Chequers” as he warned of a dismal future of European industry controlling the UK.
He said: “It cannot be repeated too often that under the Chequers proposals for ‘ongoing harmonisation’ and a ‘common rulebook’ this country is offering Brussels and the powerful European industrial interests behind the Commission the chance to control huge chunks of UK industry, to stifle innovation, to run our trade and commercial policy, to collect UK taxes – and with no British voice round the table to raise even a peep of protest.
“It is quite incredible that the Cabinet remains acquiescent. We must chuck Chequers forthwith.”