It will take the British province of Northern Eire out of the EU's customs union however preserve it largely aligned with the bloc's "single market" requirements and rules. A spokesman for the German chancellor confirmed the call had taken place but declined to comment further.
He added that the Chancellor and the German government are "good friends" of Britain. "Frankly a deal on the basis of Johnson's proposals by October 31 has been unrealistic from the beginning.", he said on Twitter.
The pound had jumped more than 0.5% against the USA dollar after the Times newspaper published its report, but the chief whip of Northern Ireland's Democratic Unionist Party said it would oppose any such concession, sending sterling back down to $1.2210, flat on the day.More news: Dozens of climate activists were arrested for blocking downtown Montreal streets
Tusk asked the United Kingdom prime minister where he meant to go with the intractable issue seeing as "you don't want a deal, you don't want an extension, you don't want to revoke".
A senior diplomat dismissed the Times report as "spin" in the negotiations, while another official said that "no bold new offer is coming from the European Union side at this stage".
Irish Foreign Minister Simon Coveney too said that he found it "hard to disagree" with Tusk, with reports indicating that Dublin is unwilling to strike a deal with the UK.
Varadkar was keen to stress, however, that while he would "certainly work until the very last moment" to secure a deal, it would not be at "any cost" to Ireland, Northern Ireland or the rest of Europe.
An array of remarks by unidentified British sources laid bare just how far apart the two sides are after three years of tortuous haggling over the first departure of a sovereign state from the EU.
Sterling jumped more than 0.5% against the us dollar on Wednesday after the Times newspaper said the European Union was ready to agree to a major concession in Brexit negotiations.More news: How much each golfer won at the Shriners Hospitals for Children Open
Downing Street sources accused Mrs Merkel of torpedoing a Brexit deal by insisting that Northern Ireland remained in the customs union indefinitely.
As a result of the apparent political deadlock, firms that are primarily focused on the British market and listed in the London Stock Exchange suffered on Tuesday: from Tesco supermarket and airlines to house building societies, there was a nosedive.
Nor does it matter that any serious analysis of Johnson's "two borders for four years" proposals (with a regulatory border in the Irish Sea and a customs border on the Irish mainland) would immediately identify its impossibilities.
On Tuesday, Britain published more details of its plans for a scenario where there is no deal.
Johnson says Britain will leave without a negotiated settlement if a deal can't be reached by the Brexit deadline of October 31.
Anti-Brexit campaigners fear Johnson will try to wriggle out of that requirement, and asked Scotland's highest court to order the government to comply.More news: Former US President Carter falls, requires stitches
One supply in Johnson's workplace instructed The Spectator journal the federal government will attempt to "do all sorts of things" to forestall one other Brexit delay ought to negotiations actually collapse.