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Sturgeon also hinted that she may try and block the
On Thursday, the government lost a case in the UK's High Court which ruled that May must seek a vote from parliament before it triggers Article 50, the formal legal mechanism the UK will use to leave the EU.
The government will appeal the decision, which means the case goes to the Supreme Court - and that is where the Scottish National Party (SNP) leader Sturgeon could become involved.
Asked by a colleague in the Scottish Parliament if she would "actively oppose" the appeal - by sending lawyers to act against the government in court - Sturgeon said: "We will look at the judgment very carefully and, yes, we will actively consider whether there is a case for the Scottish Government to become a participant in that case."
The government hopes its appeal will overturn the High Court decision, and allow May to trigger Article 50 using an ancient legal device called royal prerogative. Should the government lose, then it will go to a parliamentary vote - and Sturgeon hinted that she would instruct her party to vote against it if that does happen.
Scotland voted to remain in the EU by a margin of 62% to 38%, which Sturgeon feels gives her a mandate to try and keep the country in the EU, or at least negotiate the best possible terms. She has also threatened a second independence referendum for Scotland, arguing that Brexit amounts to a "significant and material change" in circumstances.
Sturgeon is a member of the devolved Scottish parliament, so would not be able to vote, but she could instruct her 54 SNP colleagues who have a seat in the UK parliament to vote against the bill.
She said: "Scottish National Party MPs in the House of Commons will certainly not vote for anything that undermines the will or the interests of the Scottish people."
"The job of this Government is to protect Scotland's interests. Scotland voted to remain in the European Union and my job, therefore, is to protect our place in Europe and the single market as far as I possibly can," she added.
There are 650 MPs in Westminster, however, so there is little chance that the SNP voting against the prospective bill would actually be able to influence the outcome of a parliamentary vote, unless it can rally significant support from the Labour Party, which also opposed Brexit.