The UK government has so far refused to allocate time in the House of Commons for MPs to discuss Andrew's situation in line with the royal family's wishes.
But the issue could be raised on one of the days when ministers are not in control of the parliamentary timetable.
A Liberal Democrat source indicated to Britain's Sunday Times newspaper the party could be prepared to use one of its opposition days to allow MPs to discuss Andrew's behaviour.
The prince is reportedly in discussions about leaving his Royal Lodge home voluntarily following the furore over the "peppercorn" rent for the Windsor property.
Andrew is said to be in talks with his brother King Charles' representatives but is reluctant to give up his residence of more than 20 years, with the sticking points said to be the location of his new home and financial compensation for funds spent on the lodge.
Andrew attempted to draw a line under years of controversy, following allegations he sexually abused Virginia Giuffre, by giving up his dukedom and other honours ahead of the publication of Giuffre's posthumous memoirs.
But the prince, who strenuously denies the allegations, was instead swamped by criticism that has focused on the property he has lived in effectively rent-free since 2003.
The ability of MPs to discuss matters relating to the royal family is constrained under the Commons' procedures.
The guide to the rules states, "unless the discussion is based upon a substantive motion, drawn in proper terms, reflections must not be cast in debate upon the conduct of the sovereign, the heir to the throne, or other members of the royal family".
With the government unwilling to table a motion to discuss Andrew due to the wishes of the royal family, an opposition day debate could be a way for MPs to speak out.
"We need to explore all options, including an opposition day debate, to ensure parliament can scrutinise this properly, from Prince Andrew's residence at Royal Lodge to his dukedom," a Liberal Democrat source said.
"The first thing we need is proper transparency and accountability - that's why we have called for the Crown Estate and Prince Andrew to give evidence under oath in parliament."
The Liberal Democrats have one opposition day left this parliamentary session, but no date has yet been allocated for it.
"We'll take a decision on what is most important for the national interest as and when the government tells us when it will be," the source told the PA news agency.
The Liberal Democrat insider indicated they hoped the King would be willing to take action.
"It's right that we're led by the King on this, and if parliament does have to act we hope it can be hand-in-hand with the Palace," the source said.
Although Andrew has given up using his Duke of York title, only a law passed by parliament can formally remove it.
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