But it would mean that a more formal deal like a Coalition or “confidence and supply” is ruled out.
The SNP are opposed to Trident and have made it clear that it would be a “red line” for the party in striking any deal to govern.
“I’m sure there are many issues we could work together on,” Ms Sturgeon said on the prospect of a deal with Labour on BBC Radio Scotland today.
But she added: “We know from past experience that Labour oppositions promise big and then they get into government and they don’t deliver
“If we want to make sure that Labour firstly delivers on the things that its promising to do and we agree with, we need to make sure there are SNP MPs in there holding them to account and making sure that they deliver.”
Asked if the SNP would bring down a Labour administration over Trident, she added: “You can defeat governments in a minority context, it doesn’t necessarily mean that government falls.”
A formal Coalition with Labour has been ruled out, but Ms Sturgeon said a less formal “confidence and supply” deal would require the renewal of Trident to be scrapped.
But she said: “If we were voting on a vote by vote basis, we would vote for things we agree with and we wouldn’t vote for things we don’t agree with. But under no circumstances would we ever vote for the renewal of Trident or the spending of money on the renewal of Trident.”
She said Trident is still a “red line” in terms of any formal arrangement with Labour.
But she said: “If we’re not in that position and we’re simply voting on a case by case issue, we will never ever vote for Trident. We will not vote for the renewal of Trident. The £100 billion that’s going to cost over the next 35 years would be better spent on health, education and keeping people out of poverty.”
She indicated this need not mean voting down a Labour budget, because at Westminster “budgets don’t deal with spending, they deal with tax increases.”