Irish Prime Minister Leo Varadkar, right, meets with British Prime Minister Theresa May, left, on the sidelines of an European Union and Western Balkan heads of state summit at the National Palace of Culture in Sofia, Bulgaria, Thursday, May 17, 2018.
He also said that any plan for a UK/EU shared customs area is "welcome", though work needed to go on the backstop to prevent checks on the Irish border following Brexit.
Eurosceptics will argue that the plan amounts to remaining in the European customs union by another name and will raise fears that there would be no clear end-date to links with the bloc.
Earlier, the source, who is familiar with the discussions, said on condition of anonymity the government was trying to find a way to make the backstop arrangement more acceptable to Britain rather than seeking an extension of a transition period.
"We have a text, that's the Irish backstop, which all EU27 countries stand by, and that was published in March".
However, if neither is approved and is in place when the post-Brexit transition period ends in December 2020, then Mrs May will propose a "backstop" option.
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May has been struggling to unite her cabinet over the terms of Britain's divorce with the European Union, with a row over future customs arrangement dividing her government and all but stalling Brexit negotiations.
Britain has just a few weeks before June's European Council summit to agree on a solution which would avoid a hard border between Northern Ireland and the Republic.
She said: "Once the implementation period is finished we will be able to not only negotiate and sign trade deals but implement them".
Irish Prime Minister Leo Varadkar has refused to endorse any Brexit withdrawal or transition period agreements unless the United Kingdom guarantees that there will be no reimposition of a "hard" land border with Northern Ireland, which is part of the UK. "It would help solve some of the problems related to the border but not all of them". But the move could create obstacles to business between Britain's Northern Ireland and EU-member Ireland.
The meeting, in the Bulgarian capital, Sofia, comes amid growing tension over the slow progress of Brexit negotiations.
PM Theresa May today repeatedly pleadged that Britain would leave the EU customs union in 2020.