Aileen McHarg, professor of public law and human rights at Durham University, said she previously thought the case was "arguable".
However, she said there is now more case law on devolution and the Supreme Court "has become quite conservative in its constitutional jurisprudence".
She said: "I am less confident – well, I wasn't ever confident, but I think the chances of a bill being upheld in the current climate are quite slim."
She wants another referendum to take place in October 2023, but the UK government is unlikely to agree to this.
Ms Sturgeon promised a “significant update” later this month on how a referendum can be held without the relevant powers being granted by Westminster through a section 30 order, as happened in 2014.
Under the Scotland Act 1998, the union is reserved to Westminster. However, there are different views on whether referendum legislation would fall outside the powers of the Scottish Parliament.
It is widely expected the UK government would challenge such legislation in the Supreme Court.
Prof McHarg said the legislation would face a "two-step process".
She said: "One, you've got to get the bill into the parliament, and that's a problem because whoever is in charge of the bill has to certify that the bill is within competence.
"If it's a minister who is introducing the bill, under the Scottish ministerial code that competence certificate has to have the agreement of the law officers.
"That's hurdle number one. Assuming you get over that hurdle, and the bill gets to parliament – we can assume it will pass because of the majority in favour of it – then it can either be challenged pre-enactment by UK or Scottish law officers, or if not, it becomes an Act and it can be challenged post-enactment by anyone with sufficient interest, which in this case is really, really wide."
She added: "At the moment I think we're stuck at the first stage of actually getting the bill into parliament.
"I think we can assume that there are some difficulties in getting law officer sign-off."
Prof McHarg said a members' bill introduced by an MSP, rather than a government minister, would not need to be signed off by law officers, but would still be subject to legal challenge.
Asked about the likelihood of the Supreme Court upholding the bill, she said this was “quite slim”, explaining: "When I first wrote on this back in 2012, I thought that the case was arguable that they might uphold the validity of a bill.
"I didn't think it was by any means certain, but I thought it was arguable.
"Since then we've had quite a lot more jurisprudence, a lot more case law from the Supreme Court on devolution.
"We're also in a period where the Supreme Court has become quite conservative in its constitutional jurisprudence.”
The legal expert said the “fundamental point that you simply can't get over is that the UK Parliament has to agree to dissolve the union”.
However, she argued: "That doesn't mean that a unilateral process is completely pointless. It can serve a political purpose, it can continue to put pressure.
"I think some of the arguments about a unionist boycott are quite risky in themselves, because if a referendum goes ahead, it will only go ahead if the Supreme Court has held that a referendum bill is lawful.
"If the Supreme Court holds that it's unlawful, there just won't be a referendum, so there will be nothing to boycott.
"So you'd be talking about boycotting something that has been argued in court and the Supreme Court has said is lawful.
"To boycott that is risky from a unionist perspective as well."
Prof McHarg said the UK government could amend the Scotland Act "to make it clear that a referendum is outwith competence", although by doing this it would take a “pretty big political hit”.
David Phillips, of the Institute for Fiscal Studies, said an independent Scotland could face tax rises or spending cuts.
He added: "Unless the oil revenues stay high – if they go back down, I'd be fairly confident that you would be looking at tax rises or spending cuts, maybe not immediately, but it would need to happen in the first decade of an independent Scotland."