Mr Yousaf said the UN could be called in, or a third party country trusted by both the Scottish and UK Governments
First Minister John Swinney has said he is “thinking about” a proposal from his predecessor on the process for a new independence referendum.
Humza Yousaf, who served as first minister for just over a year, said last week that a third party should be invited to decide the trigger point for another vote.
In recent years, much of the debate has focused on how and when another poll could be initiated with independence supporters keen to bring the debate back to the idea of the leaving the UK.
In interviews to promote his new book, Mr Yousaf said the UN could be called in, or a third party country trusted by both the Scottish and UK Governments.
But the plan has divided the SNP, which meets in Aberdeen on Thursday as its annual conference opens.
Mr Swinney said: “I think there’s some interesting points that have been raised by Humza Yousaf with that suggestion and I think I want to have a discussion about the substance of independence because I think that’s what makes a difference in people’s lives.
“We have spent a long time talking about process, so I think what Humza Yousaf suggests is an interesting idea about how to perhaps take the process issues away to somewhere else and to concentrate on the substance.”
Asked if he planned to pursue Mr Yousaf’s proposal, the First Minister added: “I think it’s an interesting and substantial proposition, so it will be something that I’ll be thinking about.”
But the plan was criticised by former SNP MP Stewart McDonald, who said in a post on X the “third party too often overlooked by both sides is the people of Scotland”.
“We should never seek to export our own domestic political issues to another body or state to resolve,” he said.
“This is not a violent conflict or civil war requiring international mediation – it is a democratic, political disagreement, however deep the passions run.
“Are we really saying that Scotland is a problem for others to fix, rather than a positive participant in helping solve the many global challenges of our time?
“It’s an absurd proposition that I think both pro-Union and pro-independence camps can rightly repudiate.”
The conference, which will see Mr Swinney address party faithful on Saturday, is the first since the guilty plea of former chief executive – and Nicola Sturgeon’s estranged husband – Peter Murrell, who was jailed for embezzling more than £400,000 from the party during his time in charge.
But Mr Swinney said he will not have to take a softer approach with members following what he has previously described as a “hugely damaging and traumatic experience for my party”.
“I’ve addressed that trauma very directly with the party membership and I’ve done that in a number of ways,” he said.
“We’ve had some very open dialogue within the party about these questions.”
He added: “Members of the party, they know me well, they know what I expect, they can see the results of that, because I promised them good governance and they’re getting that.
“I promised them an election-winning machine, they’ve just seen that in action.
“I think the party, although injured by all of what’s happened, has also had my reassuring leadership to help it through that.”