The devolved administrations have said they cannot recommend that legislative consent is given to the European Union (Withdrawal) Bill as it stands.
The legislation - designed to transpose EU law into British law so the same rules apply on the day of Brexit as the day before - will see EU responsibilities in devolved areas initially transferred to Westminster.
The Scottish and Welsh governments said it amounts to a power-grab, and must be amended to give certainty to businesses, citizens and to protect devolution.
Scotland’s Brexit Minister Michael Russell and Welsh Finance Secretary Mark Drakeford will be joined at the meeting by the Scottish Government’s Lord Advocate James Wolffe QC and the Welsh Government’s Counsel General Mick Antoniw.
It comes after Scottish First Minster Nicola Sturgeon and Welsh First Minister Carwyn Jones teamed up to oppose the Bill when it was published earlier this month.
Speaking ahead of the meeting, Mr Russell said: “The European Union (Withdrawal) Bill is quite simply an attack on the hard-won powers of the Scottish Parliament and on the principles of devolution.
“We cannot and will not stand by and let powers in devolved areas be taken by the UK Government. The Bill must be changed to respect devolution and our parliament.
“I look forward to discussing how we can protect devolution with Professor Drakeford and our priorities for amending the Bill.”
Professor Drakeford said: “The Welsh Government’s position has always been that we agree there is a need for an orderly exit from the EU, but that it needs to be based a set of arrangements that gives certainty to businesses; to our communities and respects the devolution settlement.
“The EU Withdrawal Bill does absolutely none of those things as it is currently drafted and the UK Government cannot expect the support of the devolved administrations on that basis.”
The UK Government has said it intends to respect the devolution settlement as powers are returned from the EU under Brexit.
But it has said it is necessary to bring powers back to Westminster before devolving them in order to develop common frameworks and prevent trade barriers being created within the UK.
A UK Government spokesman said: “We have been clear that the Repeal Bill will not take away any decision-making powers from the devolved administrations immediately after exit.
“Instead, to protect the UK internal market, some decision-making powers being transferred into UK law will be held temporarily to allow intensive discussion and consultation with the devolved administrations.
“As the Secretary of State has made clear, it is our expectation that the outcome of this process will provide a significant increase in the decision-making power of each devolved administration and we are committed to positive and productive engagement with the Scottish Government.”