May, who might make a fourth attempt to win Parliament's support for her deal this week, is considering calling a general election to help break the Brexit deadlock.
Her Cabinet is split, with some ministers urging her to take the UK out of the EU without a deal on April 12 and others saying they'd quit if that becomes her policy.
Merkel's talks with Varadkar come amid increasing concern in Germany that Ireland hasn't made sufficient preparations to protect the Irish border - the EU's new external frontier after Brexit - in the event of no-deal.
At an EU summit 10 days ago, Merkel admonished Varadkar for Ireland's lack of a plan, officials said. Ireland still doesn't acknowledge how urgent the situation is, according to one of the officials.
After trying to remain above the Brexit fray since negotiations between the UK and EU began almost two years ago, Merkel is becoming much more active, as the threat of no-deal looms.
Underlining the frustration in Berlin with the situation, Deputy German Foreign Minister Michael Roth yesterday accused "90 per cent" of the British Cabinet of having "no idea how workers think, live, work and behave" because they were "born with silver spoons in their mouths".
Merkel's role will also prove crucial if the UK requests a long Brexit extension. Germany is one of several countries willing to give Britain time, especially if May calls a snap election, according to officials. French President Emmanuel Macron has argued against such a move. Approving a Brexit delay would have to be unanimous among the 27 EU leaders.
The critical need to prevent a "downward spiral" from turmoil in London and a potential no-deal exit from damaging the rest of Europe is now the priority of the EU's 27 remaining governments, according to a diplomatic note of talks between envoys in Brussels last week.
The Irish border issue has become an almost intractable problem. The EU's proposed "backstop" arrangement, contained in the Brexit deal rejected three times by the British Parliament, is aimed at preventing the need for infrastructure and visible checks on the frontier by keeping the UK in a customs union with the bloc until a replacement solution is found.
But Ireland, which insists there can be no return to a hard border - a symbol of decades of violence which ended with a peace accord in 1998 - has been reluctant to spell out what would happen if the Brexit deal fails.
The EU will oblige Ireland to check the flow of goods across the frontier because of Ireland's place in the bloc's customs union and single market, but officials are working on ways to ensure this can happen as much as possible away from the border, people familiar with the matter said.
- Bloomberg