The proposal would see the Connecting Europe Facility adapted to ensure Member States' ports can still like to Ireland; and to provide financial support for border security.
During the 1960s, a political division began over the constitutional status of Northern Ireland; for almost 40 years, a violent ethno-nationalist conflict between the Nationalists (for one Ireland, a nation state), Republicans (mostly Catholics) against Unionists (political union with UK) and Loyalists (mainly protestant monarchists opposing a United Ireland) continued.
"If we were in the backstop, it would be quite hard for us to engage with partners, not knowing when the end date would be when we could implement any agreement", he said on a trip to Northern Ireland. The recent history of a militarised border.
But he said he had voted for the deal already, "so I can't be bribed". "The Withdrawal Agreement is not open for renegotiation", EU Council President Donald Tusk tweeted.
Currency traders also took that view as sterling traded around $US1.307, more than a cent down from the level reached before MPs voted.
Dankse Bank is one of the big four banks in Northern Ireland, and provides around 20% of mortgages there. "We're asking for money for areas that have not had their fair share in the past", he said.
European Union leaders have so far expressed an unwillingness to reconsider opening up the withdrawal agreement.
She said: "This is about protecting a peace process". She aims to get parliament's approval for a revised deal on February 13. "There is a symbolic majority in the British parliament against no deal but no majority for anything that would avoid it".
Verhofstadt, one of the EU's most vociferous defenders, did not, however, close the door on the possibility of discussing with the United Kingdom the future relationship between the two sides. "It is against a no-deal Brexit, it is against a backstop".
A Labour spokesperson said the two would meet again "soon" after the 45 minutes of "cordial" talks in the prime minister's Commons office. But the PM believes the issue has not been settled and further votes will be put to the Commons in an attempt to force an agreement and avoid a "no-deal" scenario.
"At this point, I am gravely concerned about the challenges ahead should a hard Brexit become a reality".
He will also use the opportunity to thank the European Union institutions, and other member states, for their "continuing support" for Ireland, the Taoiseach's office said.
This would give May "the mandate I need to negotiate in Brussels... a significant and legally binding change to the Withdrawal Agreement", she said.
The EU's chief Brexit negotiator, Michel Barnier, then addressed the parliament, telling lawmakers that the Irish backstop was part and parcel of the withdrawal agreement and would not be re-negotiated.
On Wednesday, May met opposition Labour Party leader Jeremy Corbyn to discuss the situation the country faced.
Mr Varadkar reiterated his government's stance on no deal during a phone call with Mrs May on Wednesday afternoon.
It still remains unclear.
May now has several weeks to persuade the European Union to change its mind on the Irish backstop arrangement.