Last month, Parliament voted in favour of an amendment that supported most of the PM's deal but called for backstop - which is a last-resort option to prevent a hard border in Ireland - to be replaced with "alternative arrangements".
His remarks to reporters came after talks with EU Brexit negotiator Michel Barnier.
The agreement finalized on Friday should remove the uncertainty a "hard" Brexit scenario posed for some 15,000 citizens of the three non-EU nations who live in Britain.
"We are absolutely clear on this: we're not considering Jeremy Corbyn's customs proposals, we're not considering any proposals to remain in the customs union".
"It is time for Dr Fox to face facts and admit this - particularly to businesses, who are in urgent need of proper guidance".
Meanwhile, Mrs May has offered further talks with Labour in an attempt to secure cross-party consensus on Brexit.
May has indicated, to the fury of Brexiters, that she is prepared to negotiate with Corbyn, raising their suspicions she might opt to ask the EU for Britain to remain permanently in the customs union, a deal she could get the Commons to endorse by seeking cross-party support.
There were also signs of unease in the Tory ranks at the idea of Mrs May exploring means to bring the Labour leader on board efforts for a Brexit deal.
Aaron Ramsey 'signs £400k-a-week Juventus deal'
But he has now committed to a four-year contract with Juventus and will join the Italian champions at the end of the season. Wages were not disclosed, but Goal understands Ramsey will earn €7 million (£6m/$8m) plus bonuses per year.
But in efforts to build cross-party support for a Brexit deal, she offered flexibility on Corbyn's calls to keep up with European Union measures to protect the environment and workers' rights, asking for further talks with Labour "as soon as possible".
The wording of May's motion on Thursday, asking Parliament to back her negotiation, will be closely read.
"Former Conservative chairman Grant Shapps warned in a tweet: "(The) coalition worked hard to create a dynamic United Kingdom jobs market & we enjoy half the unemployment rate of France by being a more attractive place to hire people.
Together with a group of Labour backbenchers encouraged by promises of fresh guarantees on workers' rights and environmental standards, May hopes she can win over enough MPs to pass her deal.
With 45 days to go until Britain is due by law to leave the European Union, with or without a deal, the prime minister will address MPs about progress in the Brexit talks, No 10 announced on Monday.
He said: "You can't stop no deal unless you have got something else to replace it".
Britain and Switzerland will sign an agreement on Monday to continue trading on preferential terms after Brexit, the British trade department said, protecting a trade relationship worth 32 billion pounds, Trend reported citing Reuters.
The UK and Switzerland have signed a deal to continue trading after Brexit as they did before it.