The German foreign minister also rejected British attempts at obtaining further concessions that can satisfy hardliners and critics of the deal in London.
May also said that she is determined to deliver Brexit, and determined to deliver on time on March 29, 2019.
In an article in the Sunday Telegraph, the Prime Minister said that she would be going to Brussels to with a "fresh mandate, new ideas and a renewed determination" to stick to the agreed United Kingdom departure date on the 29th March.
May said she is determined to deliver Brexit on time. The leaders are to discuss preparations for a no-deal Brexit in the event that the withdrawal agreement is not ratified.
Opponents to Brexit were quick to seize on the Sky News claim, which the firm said it would not comment on.
"The EU will not renegotiate the withdrawal agreement and there will be no withdrawal agreement without the backstop", he wrote, adding that the backstop was required to "ensure the protection of the Good Friday Agreement".
Several rebellious centrist Labour MPs, who want a soft Brexit or to stay in the European Union, are mulling forming a new party, according to Sunday's Observer.
The head of government wrote in the newspaper: "I'm going to be armed with a fresh mandate, with new ideas and new determination, to agree to a pragmatic solution that provides the Brexit, the British people voted, and at the same time ensures that there is no hard border between Northern Ireland and the Republic of Ireland".
Fox echoed comments by Foreign Secretary Jeremy Hunt on Thursday that a delay to the March 29 leaving date may be needed in order to get legislation through parliament.
Our political correspondent Chris Mason said that while Mrs May pledged to "go back to Brussels to secure a plan that Parliament can stand behind", the European Union remains publicly opposed to changing the backstop. She wrote that Now that "the British public wants us to get on and finish the job", and "the vast majority just want MPs to set out a clear plan that will get Brexit through Parliament and allow us to embark upon the next chapter of our national story".
"That's what I'd like the most", he said.
Javid said: "You can have no hard border on the island of Ireland and you can use existing technology, it is perfectly possible".
"There is a deal on the table, and walking away from it will have serious consequences for us all".