President of the European Parliament Antonio Tajani said he hopes "common sense will prevail".
"We have done everything possible to reassure the United Kingdom. We look forward to a positive vote in the Commons," he tweeted.
READ MORE: Brexit: Theresa May breaks Irish backstop deadlock with EU
Mr Tajani met with Mrs May in Strasbourg on Monday night.
After the emergency cabinet meeting concluded in Dublin late on Monday night, Transport Minister Shane Ross said the Taoiseach would make a statement on Tuesday morning.
"I think everybody here is hoping that it goes through the House of Commons tomorrow," he said.
"I think that's what we're hoping for.
"We're very hopeful that it will go through."
Independent Group MP Chris Leslie said the Government's "Brexit fudge fools nobody".
"They can't reconcile the irreconcilable objectives of ditching Single Market & Customs Union...while keeping Irish border open & frictionless," he wrote on Twitter.
The group of 11 former Labour and Tory MPs has tabled an amendment to the motion to be debated, calling for an extension to Article 50 so Parliament can agree the terms of a so-called People's Vote.
READ MORE: Brexit: How did MPs react to Theresa May's 'legally binding changes to EU deal'
Mr Juncker and chief negotiator Michel Barnier briefed the European Parliament's Brexit steering group after the EU Commission president's press conference with Mrs May.
The Commission's chief spokesman, Margaritis Schinas, tweeted a photo of the group.
The Prime Minister has arrived back at Downing Street after returning from Strasbourg.
Mrs May is expected to chair a Cabinet meeting on Tuesday morning before the motion is debated in the Commons in the afternoon and votes are held in the evening.
Dutch Prime Minister Mark Rutte said he hoped MPs at Westminster would back the deal as "there is no alternative".
"An orderly Brexit is crucial for both the EU and the UK," he said.
"I hope that the House of Commons will support the agreement reached by Theresa May. There is no alternative."
Former Tory leader Iain Duncan Smith told BBC Radio 4's Today that Brexiteer legal experts were examining the detail of the documents.
He said concessions on the backstop were needed in order to strengthen the position in the next phase of talks on a future UK-EU trade deal: "If it is correct that this backstop is both temporary and we can leave it at the moment of our choosing, that means we become a balanced partner in the negotiations.
"That is how critical this really is. What we decide today will decide whether or not we will get a good relationship afterwards or whether we get spoon fed what the EU wants us to be."
He suggested the Commons vote should be delayed for 24 hours in order to give MPs more time to assess the details of the agreement.
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