The survey, carried out during the height of the row over the Finance Secretary’s beliefs, showed 28 per cent of people who voted SNP in 2021 would like to see her become leader.
Only 20 per cent said they wanted to see Mr Yousaf become the party’s next leader and first minister, with the third candidate in the race, Ash Regan, adrift on 7 per cent.
However, almost a third (31 per cent) of those who voted SNP at the last Holyrood election said they had yet to make up their mind on who their preferred candidate was.
The poll of 1,001 Scottish adults who voted SNP in 2021, commissioned by communications agency the Big Partnership, was conducted between Monday and Wednesday of this week.
The survey’s results suggest that claims Ms Forbes instantly torpedoed her own campaign by stating her views on same-sex marriage and having children out of wedlock are premature.
She triggered a major backlash after saying on Monday that she would have voted against same-sex marriage legislation if she was an MSP at the time it was passed in 2014.
She went on to say that having a child outside of marriage “would be wrong according to my faith” and is not something that she would personally ever do.
The row resulted in Ms Forbes being abandoned by many of her key earlier supporters in the SNP, with some saying they could never vote for a first minister with such views.
In a statement addressing the issue on Thursday, the Finance Secretary sought to draw a line under the poor start to her campaign, saying she was “greatly burdened and heartsore” that her comments had “caused hurt” to some of her friends and colleagues.
“That was never my intention, but I’ve listened carefully,” she added. “I will protect the rights of everybody in Scotland, particularly minorities, to live and to love without fear or harassment in a pluralistic and tolerant society. I will uphold the laws that have been hard won, as a servant of democracy.
“I will also seek to enhance the rights of everybody to live in a way which enables them to flourish.”
But in a sign that Mr Yousaf’s campaign wants to keep the focus on Ms Forbes’s views, one of his key allies, Neil Gray, said she “had to recognise that her views don’t chime with the majority of people in both the party and the country”.
He added: “Scotland needs a leader who minorities in our society know will protect and promote their rights at all times.
“It’s important that our party picks a leader who can be elected as first minister to serve all of Scotland and who all voters know will have their back.”