The Scottish Greens said at the weekend they will quit the government if the new first minister does not share their "progressive values".
Co-leader Patrick Harvie said they were a necessity if the power-sharing agreement with the SNP was to continue.
The other co-leader Lorna Slater said a commitment to climate justice and trans rights were "non-negotiable".
Ms Slater said she wanted the Greens to stay in government and continue their work. "But not at any cost," she added.
The Greens and the SNP signed the Bute House Agreement in 2021, which was hailed by Ms Sturgeon as a "new and better way of doing government".
The BBC says the Green politicians' comments at the weekend are seen as the clearest signal yet that they would not work with Kate Forbes or Ash Regan, who are also standing to replace Nicola Sturgeon. Humza Yousaf is the only one of the three SNP leadership candidates who has committed to continue the agreement.
The result of the SNP ballot will be announced later today.
Big drinks firm ask new FM not to bottle it on DRS launch
Soft drinks firms including Coca-Cola, PepsiCo and the maker of Irn Bru have urged the next first minister to deliver a recycling scheme on time.
The British Soft Drinks Association asked the new leader to make the deposit-return scheme a "top priority".
All three candidates hoping to succeed Ms Sturgeon have raised concerns.
A BSDA spokesman said: "Please focus on ironing out the kinks, maintaining a level playing field and delivering the scheme on time."
The BBC says Scotland is aiming to be the first part of the UK to introduce a deposit return scheme for single-use drinks containers.
A 20p deposit would be paid by consumers, who would get their money back when the empty containers are returned.
Extra costs
Many businesses have said previously that the scheme will place extra costs and other burdens on them at a time when they are already struggling.
All three SNP leadership contenders now say the initiative will not go ahead in its present form - Ms Forbes and Ms Regan want it paused, while Mr Yousaf would exempt smaller firms for a year.
Lorna Slater, the Scottish Greens minister leading the scheme, says she is "actively considering" such a grace period for small businesses.
The scheme is due to go live on August 16.