It reportedly states that in the wake of Britain crashing out of the European Union without a deal, for months after, the Government may have to engage in a 24/7 emergency approach.
He added that Britain's only path to avoiding a so-called "hard Brexit", in which London exited automatically on March 29 with no transitional arrangements in place to ensure the continued flow of goods, medicines and transport links, was to accept the existing deal.
Late last month, the MPs voted in favour of an amendment that was tabled by Sir Graham Brady to look for "alternative arrangements" to the Irish backstop after the MPs turned down the Brexit deal of the Prime Minister by historic margins last January.
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.
"If I return to Brussels, I will fight for great Britain and Northern Ireland", wrote May in the "Sunday Telegraph".
"I will be armed with a fresh mandate, new ideas and a renewed determination to agree a pragmatic solution that delivers the Brexit the British people voted for, while ensuring there is no hard border between Northern Ireland and the Republic of Ireland", she wrote.
On Wednesday will vote on EU-great-grandson, Donald Tusk, with the Irish Prime Minister, Leo Varadkar. "There must not be a hard border to the Republic of Ireland".
Under the current Brexit deal, the 310-mile Irish border would become the only land border between the European Union and the UK.
If such an agreement could not be reached, then to avoid those checks and border posts or other infrastructure, the backstop would come into force.
"That is what Parliament instructed me to do on Tuesday night", May said asserted.
Mrs May argued that under the current Withdrawal Agreement the European Union has already accepted the principle of alternative arrangements to supercede the backstop should it ever be required.
She rejected any suggestion that seeking alternative arrangements to the backstop constitutes "ripping up the Good Friday Agreement".
And our correspondent added that the United Kingdom has not yet publicly suggested an alternative Brussels could live with.
In the interview with the Funke media group, Maas repeated the EU's position that the withdrawal agreement thrashed out between Brussels and London, which was rejected by Britain's parliament last month, could not be renegotiated. May's withdrawal agreement by 432votes to 202, with almost 120 Conservative MPs voting against their leader.