Scotland on Sunday claims the SNP will be making the proposal when it unveils its legislative plans later this year.
A 40p minimum would effectively mean that a bottle of spirits could not be bought for less than £10.40. The effect on cheap bottles of white cider would be more marked, but wine and beer prices would not be affected.
There have been calls from some quarters for the Scottish government to back a 50p minimum unit price, meaning the SNP could face pressure throughout the summer to take a tougher line.
Many in the drinks industry believe any form of minimum pricing would breach European competition law. But any legal challenge to a policy introduced in Scotland would have to be brought against the Westminster government, which has shied away from minimum pricing in its proposed code of practice for alcohol retailing.