Theresa May is expected to meet DUP leader Arlene Foster in London before heading to Dublin to meet the Taoiseach on Wednesday evening.
It comes amid mounting speculation that the Prime Minister is fighting to not only to save her Brexit deal but potentially her leadership.
Rumours of a backbench coup against the Conservative leader are swirling around Westminster.
Owen Paterson is the latest MP to say he has written to 1922 Committee chairman Sir Graham Brady.
- READ MORE: What is the 1922 Committee?
The Prime Minister has already held talks with other European leaders and EU officials in an attempt to salvage her Brexit deal.
On Tuesday, Theresa May met with German chancellor Angela Merkel, Dutch prime minister Mark Rutte, European Council president Donald Tusk and European Commission president Jean-Claude Juncker.
It follows her decision to call off a crunch Commons vote on the deal, which had been scheduled to take place on Tuesday, after admitting she faced a "significant" defeat on it.
The vote on the withdrawal agreement was called off so assurances could be sought from Brussels over the Irish border backstop.
Theresa May will fly out on Wednesday evening to Dublin for talks with the Taoiseach Leo Varadkar, before travelling on to Brussels for a summit of EU leaders starting on Thursday.
Before heading to Ireland, she is due to chair the weekly meeting of the Cabinet – postponed from Tuesday – as well as holding talks with DUP leader Arlene Foster, whose party props up her minority Government in the Commons.