The businesswoman, who successfully challenging the Government’s right to take Britain out of the European Union without parliamentary approval, said she would be willing to fund another lawsuit.
Speaking on BBC Radio 5 Live Daily Ms Miller said: "It is my money and my decision and my actions, and I can't think of anything better to do with the success I have."
It came as campaigners opposed to a so-called "hard Brexit" have obtained legal advice that Britain's "actual withdrawal" will have to be authorised by a fresh act of Parliament.
The Government suffered its first defeat over the Brexit Bill on Wednesday when the House of Lords backed an opposition amendment guaranteeing the future status of EU nationals living in the UK.
Ministers immediately signalled their intention to overturn the vote when the legislation goes back to the House of Commons later this month.
Before then, however, they are facing the prospect of a second defeat in the Lords next week on another opposition amendment which would require the Government to give Parliament a "meaningful" vote on Britain's final withdrawal.
While Mrs May has promised a vote on any agreement with the EU, opposition parties as well as some pro-Remain Conservatives, fear that if there is no deal Britain would simply crash out of the EU with Parliament unable to intervene.
Ahead of next week's vote, the Open Britain campaign group sought to stiffen opposition in the Lords, circulating peers with details of legal advice it has obtained from three leading QCs - Sir David Edward, Sir Francis Jacobs and Sir Jeremy Lever.
According to the group, the advice states "actual withdrawal" will require a "full act of Parliament" once the terms of any deal are known and that legislation would also be required if the Brexit negotiations ended without an agreement.
The threat of further legal action will infuriate pro-Leave MPs who believe the attempt to write the requirement for a vote on to the face of the Bill is designed to derail the whole Brexit process.
Despite the latest challenge, Brexit Secretary David Davis - in Copenhagen for talks with Danish foreign minister Anders Samuelsen - said the process remained "on track" for the Government to invoke Article 50 by Mrs May's deadline of the end of March.
"The most important thing in this is that we will conclude in time to present the Article 50 letter and will do so in terms that are in the interests of both ourselves and the European Union," he said.