Mr Varadkar met Sinn Fein Finance Minister Conor Murphy and SDLP leader Colum Eastwood on Wednesday, ahead of the meeting with Sir Jeffrey on Thursday.
But the DUP leader said the meeting will be “meaningless” unless Mr Varadkar adopts a new approach on the Northern Ireland Protocol.
The protocol, part of the Brexit divorce deal agreed by the UK and Brussels, effectively keeps Northern Ireland in the EU’s single market for goods.
This means checks on goods being sent from Great Britain into the single market and in some cases could result in prohibitions on certain products that do not comply with EU rules.
The protocol was put in place to ensure there would be no hard border with Ireland, but it has instead effectively placed a trade barrier in the Irish Sea and is deeply unpopular with unionists who have insisted it should be removed.
Sir Jeffrey said: “A fresh visit from Leo Varadkar to Northern Ireland will be meaningless unless he comes with a fresh approach.
“He has championed a protocol which fundamentally undermines the Belfast Agreement and he has dismissed economic and constitutional concerns with patronising comments about the colour of our post boxes.
“It was Leo Varadkar as the then taoiseach who insisted on such arrangements with fellow EU leaders. If the Irish Sea border remains, then Mr Varadkar will return as taoiseach with a legacy of relations between Northern Ireland and the Republic fundamentally undermined and political progress in Northern Ireland reversed.
“Mr Varadkar faces a choice: he can continue with the rhetoric of recent years and watch those events unfold or he can adopt a new spirit of positive co-operation.
“Arrangements which respect both the EU single market and Northern Ireland’s place within the UK internal market are not just achievable but would deliver on the promise of protecting the Belfast Agreement.”
Mr Varadkar is also meeting business representatives during his visit to Northern Ireland.
Meanwhile UUP leader Doug Beattie said tonight that he had discussed the NI Protocol with Mr Varadkar.
“Today, along with Lord Empey, I met with Tánaiste Leo Varadkar who is in Northern Ireland to meet party leaders,” he said.
“The conversation covered a number of topics including the effects of COVID, particularly on tourism on both sides of the border. We discussed legacy, our belief that the Irish Government should do more on this issue and reiterated our opposition to any form of amnesties. The meeting was good natured, friendly and productive.
“We spent time talking about the Ireland/Northern Ireland Protocol. We pointed out the negative effects the protocol is having on community relations and the fine balance of the Belfast Agreement. We also acknowledged that for some businesses access to both the EU and the UK single markets was extremely positive, but checks were having clearly detrimental effects on other businesses.
“We pointed out that we believe that the UK Command Paper published in July had many positive aspects contained within it and should be viewed as a template for a way forward. We also promised to send the Tánaiste a copy of our own revised proposals that use the Belfast Agreement as a means of dealing with both the trade issues contained within the protocol and the democratic deficit.
“As ever the Ulster Unionist Party does not just complain about problems and difficulties. Instead we continue to look for solutions in order to play a positive part in getting rid of the protocol. This requires replacing it with something that can be transformational for Northern Ireland, maintains our place within the United Kingdom and protects the EU single market. It is achievable if the will is there.”
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