The EU has said the Brexit deal will “not be renegotiated” ahead of the crunch Commons vote in mid-January.
Theresa May has been attempting to secure changes to the agreement in order to persuade Tory MPs to back the deal.
It comes as Environment Secretary Michael Gove stepped up warnings that a no deal Brexit would have “grim” consequences and cause “considerable turbulence” to British agriculture.
The prime minister faces an uphill battle to convince her party and others to accept the backstop proposal, which would see Northern Ireland adhere to an EU regulatory framework if a wider trade deal between the UK and EU can not be agreed.
But critics of the backstop believe the plan would undermine the constitutional integrity of the UK by creating an economic border between Northern Ireland and Great Britain.
In a blow to May, a spokesperson for EU Commission President Jean-Claude Juncker said on Thursday said the current agreement was the “best and only deal possible”.
“For now no further meetings are foreseen between the commission’s negotiators and the UK negotiators as the negotiations have indeed been concluded,” the spokesperson said at a press conference in Brussels.
“We are not renegotiating what is on the table. Our solutions are on the table, we are ready to listen but at this stage there are no further meetings and the EU 27 leaders have been very clear that it will not be renegotiated what is on the table.”
According to the Financial Times, May is expected to speak this week to EU leaders including German chancellor Angela Merkel, Dutch prime minister Mark Rutte and European Council president Donald Tusk in an attempt to break the Brexit logjam.
MPs are due to vote on the deal at some point in the week beginning January 14.
It had initially been due to take place on December 11, but the prime minister delayed it after accepting she would lose.