Prime Minister Theresa May will meet with Scotland's leader Nicola Sturgeon amid an independence dispute and ahead of Brexit.
Barnier said that once an agreement was made the European Union could look to building a partnership with the UK. "My position isn't going to change, which is that now is not the time to be talking about a second independence referendum".
Asked what would happen if her call for another referendum was rejected by the British government, Sturgeon said: "I will set that out in due course".
Open Europe said the Prime Minister should pull Britain out of the union entirely before striking a new "customs facilitation agreement" as part of a comprehensive free trade deal, similar to those enjoyed by Switzerland and Canada.
May's London-based government must approve a legally binding referendum, and May says "now is not the time" for a new independence vote. Labour's shadow Brexit secretary Keir Starmer on Monday outlined six tests the final Brexit deal would have to pass for the party to support it.
Theresa May has vowed to build a "more united nation" after Brexit while on a visit to Scotland.
"The "exact same benefits" is an exacting standard". And it is one we will hold them to.
The veteran French politician has previously served as European Union commissioner for internal market and services and also regional policy.
It said Wales, backed Leave by a majority of 52.5 per cent to 47.5 per cent in last year's referendum, could be the biggest loser because of its reliance on European funding.
"Walking away from a deal in a typical free trade agreement (FTA) scenario would leave both parties [the United Kingdom and EU] no worse off than when they came to the negotiating table", said Terry Scouler, CEO, EEF.
Ms Sturgeon only mentioned Section 30 - the legislation which could allow her to hold a referendum on independence - "briefly at the end" of the meeting and the Prime Minister's views are "well known on this issue", the source said.