Mr Russell said he detected “stronger sympathy” for the cause among EU nations as the former president of the European Council warned a no-deal Brexit could lead to the break-up of the UK.
Herman Van Rompuy told the Observer newspaper that leaving the EU without a deal posed an “existential threat” to the UK, with consequences for Scotland.
UK ministers have published a series of technical notices advising businesses and the public on how to prepare for a no-deal scenario, although they have stressed that coming to a deal with European negotiators remains their top priority.
First Minister Nicola Sturgeon has previously said she will provide an update on plans for a second independence referendum in autumn, and has said leaving the UK without an agreement would be an “unmitigated disaster”.
Mr Van Rompuy told the Observer: “The no-deal issue is not just a problem for the UK or Brussels.
“It is also an existential threat to the UK itself. One can imagine that a no deal will have a big impact and cause concern in some of the regions.
“Speaking of Scotland, it could have consequences for them and others.”
Appearing at an Edinburgh Festival fringe event, Mr Russell suggested EU leaders’ stance on an independent Scotland has softened.
Scotland’s membership status within the bloc was a key area of debate during the 2014 referendum.
Mr Russell said: “I do think that if this process is undertaken constitutionally and correctly then it will be accepted by all member states.
“But it has to be done constitutionally and correctly, and that’s what we will do.
“I do detect throughout the EU a much stronger sympathy. I do think that the scepticism of 2014 has gone away.”
Asked about the timing of a second referendum, Mr Russell said “he did not accept the premise” that the UK Government would not grant a Section 30 Order - the mechanism through which the 2014 ballot was held.
“I think that is something which is still a possibility,” he said.
He continued: “When we get to the stage where it’s Brexit or independence, people will have to be asked that question. I don’t know when that will be but I do think that will have to happen.
“As to how that happens I think that’s a matter we will have to work on in the next two to three years.”
Mr Russell went on to clarify: “I’m not setting a two or three year timetable.
“I think we are now in a position where we have to look at this almost of a daily basis, certainly on a rolling basis. So I’m not setting a two or three year timetable, nor am I setting a one year timetable.”
Speaking at a briefing last week, the Prime Minister’s deputy David Lidington said the future of the union will not be jeopardised by a no-deal Brexit.
“I think that the merits of the union of the United Kingdom are still there and are still very powerful and persuasive regardless of the outcome to the European negotiations,” he said.