The secretary of state for exiting the European Union has been invited to answer questions from MSPs on several occasions.
Nationalists are stepping up demands to see a UK Government analysis on how Brexit will impact the Scottish economy.
David Davis’ Brexit department last week refused to confirm or deny the existence of regional Brexit impact studies, but David Mundell said the information would be shared with the government in Edinburgh.
It follows publication of a London School of Economics study suggesting economic output in Scotland could fall by £30 billion over five years if Theresa May fails to secure a Brexit deal.
SNP MSP Mairi Gougeon said: “Now that we have an idea of how much Brexit is going to cost the Scottish economy, it’s time for David Davis to come and answer a few questions.
“The Europe committee in Holyrood welcomed the opportunity to discuss some of the major concerns about Brexit with the EU’s negotiator, Michel Barnier. However, it’s staggering that we’re yet to have that opportunity to speak with any UK Brexit ministers about a decision of such magnitude and with this degree of impact on Scotland.
“David Davis ducked an appearance in front of Holyrood’s Europe committee at the start of the year but the door is still open. We’d welcome the opportunity to question the Secretary of State on how he intends to protect Scotland’s interests in the negotiations and beyond.
“We have heard from David Mundell but we know he’s not at the heart of things.
“The blank paper on which David Davis campaigned for Leave remains as blank as it was 16 months ago and it’s time he came and filled in some of those blanks.”
A department for exiting the EU spokesman said: “The Secretary of State regularly appears before parliament and the Exiting the EU Select Committee answering questions from MPs of all parties.
“He has visited Scotland and is involved in a programme of close engagement with the Scottish Government, including through the Joint Ministerial Committee on EU negotiations, so that they are fully engaged in the process of planning the UK’s departure from the EU.
“The secretary of state for Scotland will appear at two Holyrood committees in the next two weeks, and the UK Government will continue to engage appropriately.”