John Swinney is expected to launch his campaign to become SNP leader and first minister later.
The MSP, who spent 16 years in senior roles in the Scottish government until last year, has already won the backing of many party colleagues.
It is still unclear whether he will face a contest for the role from the former finance secretary Kate Forbes.
The two were confirmed to have met on Tuesday, promoting speculation that a deal may be done to avoid a leadership contest.
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Mr Swinney, 60, is to hold a news conference in the Grassmarket in Edinburgh on Thursday morning, at which he is expected to confirm his bid to take over from Humza Yousaf.
Mr Yousaf announced his resignation on Monday, though he will remain in post until his successor is elected.
So far, only Mr Swinney and Ms Forbes have indicated they are considering running to lead their party and seek election as first minister.
If a run-off between them does take place, a ballot of SNP members will be required. Party officials have confirmed nominations will close at noon on the 27 May.
The Perthshire North MSP, who served as Nicola Sturgeon’s deputy for almost nine years, announced late on Wednesday that he was preparing to make a statement on speculation he would run for the leadership.
Mr Swinney was also SNP leader between 2000 and 2004, standing down after a poor showing at the European elections.
Speaking to journalists on Tuesday, Mr Swinney said he was giving the idea of running for the leadership “a great deal of thought”.
Senior party members, including Westminster leader Stephen Flynn, health secretary Neil Gray and education secretary Jenny Gilruth, have already said they would support Mr Swinney if he decides to stand for election.
Former finance secretary Kate Forbes, 34, has yet to confirm whether or not she will make any similar statement on the future leadership of the SNP.
The Skye, Lochaber and Badenoch MSP narrowly lost to Mr Yousaf in the SNP leadership election last year.
She was criticised during the campaign for revealing she would have voted against gay marriage legislation had she been an MSP at the time due to her religious beliefs as a member of the Free Church of Scotland.
At the time, Mr Swinney, also a Christian, questioned whether it would be “appropriate” for someone with such views to become SNP leader.
Several senior party members have backed her, including those regularly at odds with the SNP leadership such as Joanna Cherry and Fergus Ewing.
Speaking to BBC Scotland on Wednesday, Mr Ewing urged Mr Swinney to retract those comments.
Timetable for change
Nominations for the SNP leadership opened on Monday and close at noon one week later.
If more than one candidate receives 100 nominations from at least 20 local party branches, a ballot will be held among members to choose a new leader.
Mr Yousaf has said he will resign as first minister once a new leader is chosen. At that point, parliament will have 28 days to nominate a new first minister to be appointed by the King.
If MSPs cannot reach an agreement after 28 days, a snap election would be called.