Ian Duncan, who is expected to be appointed as a Scottish Office minster, said the devolved nations should be able to "see exactly what is going on".
UK Brexit Secretary David Davis said he was in a "constructive" frame of mind as talks with the EU began on Monday.
But First Minister Nicola Sturgeon has called for a more inclusive approach to the negotiations,
And she said warned Mr Davis that a failure to pursue the "common-sense" objective of keeping the UK in the single market would put jobs, investment and living standards "on the line".
Voters in Scotland backed the UK remaining in the EU by 62% to 38% in last year's referendum, but in the UK as a whole voters supported leaving by 52% to 48%.
Speaking to the BBC's Good Morning Scotland programme, Mr Duncan was asked whether Ms Sturgeon or Holyrood's Europe Minister Mike Russell should have a seat at the negotiating table for the Brexit talks.
He replied: "Yes, I have no problem with that. I think that should be a common approach to all the home nations so that they can see exactly what is going on."
The politician added: "But more importantly, they need to make sure that they have a seat at the discussion point in London when these positions are being hammered out because that is where the detail will be determined not actually inside the room."
Mr Duncan stood in the general election in Perth and Perthshire North, where he lost to the SNP's Pete Wishart by 21 votes.
He is expected to be appointed to the House of Lords and made a Scotland Office minister, with Tory sources saying he will bring a wealth of fishing and farming experience to the UK government as Brexit talks begin. It is not clear if he will stand down early from the European Parliament.
As the began talks in Brussels, Mr Davis said he was determined to build a "strong and special partnership" with the EU.
Subjects for the negotiations include the status of expats, the UK's "divorce bill" and the Northern Ireland border.
The UK is set to leave the EU by the end of March 2019 following last year's referendum vote.
The Scottish government wants Scotland to remain in the EU - and in particular the single market. But the UK government has insisted that Scotland will leave alongside the rest of the United Kingdom.
Speaking during a visit to University of Strathclyde research centre, Ms Sturgeon said it was "troubling" that the UK government had "no authority and no clear idea even amongst its own ranks of what it's trying to achieve" as the negotiations began.
She said: "We need to see a different approach to these negotiations if they are not going to end up being damaging to our economy.
"We need a more inclusive approach that involves voices from every part of the UK, including the Scottish government, and we need an approach that has a common-sense objective.
"In my view, that common-sense objective should be keeping the UK in the single market because leaving the EU shouldn't mean jeopardising hundreds of thousands of jobs, shouldn't mean jeopardising investment and it shouldn't mean putting living standards on the line."
Ms Sturgeon said discussions between the Scottish government and the UK government had taken place following the general election in which Prime Minister Theresa May lost her majority.
She said: "These will continue but I think it's now time, not just for the Scottish government but for voices across Scotland and across the UK, to come together to say to the UK government that they cannot continue to lead the UK down a path with no clear idea of what they are trying to achieve and a path that could be so damaging.
"So, let's have a more inclusive approach and an approach that focuses on keeping the UK within the single market."
Ms Sturgeon refused to be drawn on her plans for a second independence referendum after the loss of 21 SNP seats in the election, only saying she would continue to reflect on the result, listen to a range of different voices and come to a conclusion "in due course".
Scottish Labour MEP Catherine Stihler said there should be a "way and a mechanism" for the UK government to consult with the devolved nations on the Brexit talks.
She added: "That would mean that in the consultation, just like what the EU is doing with the parliament and the council, that the devolved nations are also involved in that consultation.
"So whatever way the UK government is going to do it I want transparency and there is no transparency about the way the UK is conducting itself."
The Scottish government should have a seat at the Brexit negotiating table, a Conservative MEP has said.