On the harder side of the Brexit debate, the former leader of the House of Commons, Andrea Leadsom, has said leaving the European Union by 31 October is her "hard red line", and in order to achieve this, Leadsom would lead a delegation of government ministers to Brussels in September to ensure that everything is in place for the UK's exit by the end of October.
Ms Sturgeon will meet EU President Jean-Claude Juncker and the EU's chief Brexit negotiator Michel Barnier after making a speech on European policy.
But her visit was mired in controversy after Foreign Secretary Jeremy Hunt said he had refused to allow Foreign Office staff to help with the logistics of the trip.
Foreign Secretary Jeremy Hunt - one of the candidates for the Conservative leadership - had asked that the Scottish government provide its own logistical support for the visit, due to concerns Ms Sturgeon was using the trip to undermine United Kingdom policies on Brexit and promote Scottish independence. There are now 10 candidates in the running for the position.
Scotland's First Minister Nicola Sturgeon said denying her support was "absurd".
Instead, she said: "We also want to contribute Scotland's ideas and talents to Europe's shared challenges and to uphold and exemplify our shared values".
Image copyright Reuters Image caption Nicola Sturgeon says Scotland is open to Europe - is the feeling mutual? Scots rejected independence by a 55-45 per cent majority in a 2014 referendum.
The then European Commission President, Jose Manuel Barosso, suggested it would be "extremely difficult" for Scotland to become an independent member of the EU. "If the United Kingdom crashes out of the European Union with no deal at the end of October, the primary responsibility lies with the Conservatives and those that advocated Brexit, but not far behind there will be Jeremy Corbyn, whose prevarication will have made it harder to avoid that outcome".
If Brexit happens, Sturgeon said, Scots, who voted heavily against it, should be given a new say on breaking from England and joining the European Union as an independent country.
Sturgeon suggested there had been a "paradigm shift" in European Union attitudes, adding, "Many people. since the Brexit vote have a deepened understanding both of why Scotland might want to be independent and what the benefits of that would be".
But it is, as the first minister put it, a different "vibe".
The first minister said that was "petty" but the United Kingdom insisted its effort and resources must be focussed on its own objectives.
Meanwhile, one of Ms Sturgeon's former advisors has warned that her chances of successfully holding a second independence referendum by May 2021 were "very remote indeed".
Ms Sturgeon is making the visit without diplomatic support from the Foreign Office, which is customarily offered for trips overseas.
A spokesman said the UK Government could not support "activities meant to campaign for policies contrary" to its position.
The revelation was dismissed by Ms Sturgeon as "childish and pathetic". "We have to confront whether the better response to that is to have the ability to be independent and shape our own future".
"Not only are they ignoring Scotland's interests, they're trying to undermine the Scottish government in trying to stand up for those interests".