First Secretary of State Damian Green is visiting the city for a meeting with Deputy First Minister John Swinney and Scotland’s Brexit Minister Michael Russell.
Scottish Secretary David Mundell will also attend the discussions, focusing on identifying where common frameworks are needed for powers returning from Brussels following Brexit.
The meeting will also attempt to identify areas in which both governments agree there should be a release of powers to the Scottish Parliament.
The UK Government argues these powers could then be released under the Repeal Bill, which has been described as a “power grab” by the Scottish and Welsh Governments.
Both devolved administrations have said they will not recommend legislative consent is granted for the Bill in its current state.
Mr Russell said: “The Bill - as it currently stands - means that Westminster would take exclusive control over significant areas of devolved policy, such as support for Scotland’s farmers and food producers and many aspects of environmental protection and control of our seas.
“We know that the UK Government has its eye on more than 100 policy areas. That is a direct threat to the devolution settlement which the people of Scotland overwhelmingly voted for in 1997.
“Both we and the Welsh Government have made it clear we could not recommend legislative consent to the Bill as it stands, and today we will make clear that changes must be made to protect devolution.
“All devolved powers currently carried out at an EU level must come back to the Scottish Parliament. We are not opposed in principle to UK-wide frameworks in certain areas - but this must be on the basis of agreement among equals, not imposed by Westminster.”
Mr Green said the meeting demonstrated his Government’s “commitment to progressing discussions”.
He added: “We want a positive and open dialogue with the Scottish Government to ensure that no new barriers emerge for people living and doing business in the UK.
“In some areas there will need to be a common approach. There will be other areas where I intend that the Scottish and UK governments can make progress in identifying policy areas that could be released to Holyrood under the new legislative arrangements.
“We expect there will be a significant increase in the decision-making power of each devolved administration and we want to address this in a way which delivers certainty and continuity for people and businesses across the UK.
“I am looking forward to serious, constructive talks with the Scottish Government on this vital matter.”
Mr Mundell added: “As we’ve made clear, the Bill sets out temporary arrangements that allow us to discuss areas where we will need to take a UK-wide approach and where new decision-making powers can be released to Holyrood.”