Taoiseach will urge May to give a 'clear' border message
In her Brexit speech last Friday, Mrs May said the UK would not accept any physical infrastructure at the border but gave few details of how this will be achieved.
The Taoiseach "cautiously" welcomed the speech which focused on Britain's offer of a two-year transition period for leaving the EU. Tomorrow, Mr Varadkar will travel to Downing Street for a bilateral meeting with Mrs May.
A senior government source said the North and the border "will feature strongly" in the Taoiseach's discussion with the prime minister.
"The Taoiseach is expected to indicate to the prime minister that, in order to demonstrate that sufficient progress has been made on Irish issues, there must be a clear and reassuring message about how the border will be avoided," the source said.
The Government is adamant there should be no border between the North and South after Brexit but such a scenario is deemed near impossible if Britain remains outside the EU customs union.
Mrs May is under pressure from her own party to take a tough stance with the EU and push for a hard Brexit which would leave Britain outside the customs union.
The Taoiseach will also use the Downing Street meeting to discuss the ongoing stalemate between Sinn Fein and the Democratic Unionist Party on restoring the power-sharing executive.
Mr Varadkar will insist Ireland will not support a return of direct rule from London.
Deadlock on restoring the Assembly has rumbled on for almost a year after Sinn Fein collapsed the institutions over the 'cash for ash' controversy.