Kate Forbes is set to leave the Scottish government after finishing second in the SNP leadership race.
Ms Forbes is believed to have been offered the rural affairs job by new first minister Humza Yousaf, but turned it down.
It means Ms Forbes, who served as finance secretary under Nicola Sturgeon’s administration, will return to Holyrood’s backbenches.
If she had moved to rural affairs it would have been seen as a major demotion, one which Forbes backer and former health secretary Alex Neil branded an “insult and not a real effort to unite”, adding: “A poor start.”
Ms Forbes narrowly missed out on the leadership, claiming 47.9 per cent of the vote in the second round.
Ash Regan was eliminated in the first round with 11 per cent of the vote.
SNP’s Kate Forbes narrowly missed out on the leadership
It comes after Mr Yousaf promised he will “argue tirelessly for independence” in his first speech after being voted into the job by MSPs.
The new SNP leader insisted his government will be “able to deliver on our priorities more effectively when Scotland is independent”.
In a sideswipe at the Conservatives in Westminster, who have blocked Holyrood reforms of the gender recognition process, Mr Yousaf also said the Scottish government would be less effective “if we allow the UK government to arbitrarily veto this parliament’s legislation”.
He confirmed later that there “absolutely will be” a minister for independence in his government, and he tipped Shona Robison, the current Scottish social justice secretary and a close ally of Nicola Sturgeon, as his deputy first minister.
Humza Yousaf, with Neil Gray and Shona Robison
Mr Yousaf said a call has been set up with Rishi Sunak “very soon”, adding: “We have a mandate for a referendum and I will be putting that case forcefully to the prime minister.”
Mr Sunak said he is “looking forward to having a dialogue” with Scotland’s new first minister.
Mr Yousaf addressed MSPs and then the media after a vote in the parliament saw him become the country’s sixth first minister, with Mr Yousaf winning the support of 71 MSPs.
In his speech to MSPs, Mr Yousaf paid tribute to his predecessor Ms Sturgeon and her deputy first minister John Swinney, who he said had “left a significant legacy”.
He told Holyrood he would be “very proud to build on the record” they had left.
