Such an appointment -– in a formal or informal capacity -– would occur within a legal gray area of the federal 'anti-nepotism' statute, according to several ethics experts consulted by ABC News.
ABC News reported Wednesday that Trump's transition team requested security clearance for Kushner the day after Trump received his first presidential daily brief, though Conway said no "formal" request has yet been made.
“It’s appropriate for whoever’s going to get the presidential daily briefing to have a security clearance,” she said. “It’s not just appropriate, necessary.”
WHAT THE LAW SAYS
The federal anti-nepotism statute at the heart of the current debate states that "a public official may not appoint, employ, promote, advance, or advocate for appointment, employment, promotion, or advancement, in or to a civilian position in the agency in which he is serving or over which he exercises jurisdiction or control any individual who is a relative of the public official."
The law sets out that the president falls under the definition of "public official" and a son-in-law falls under the definition of "relative," so legal experts say the law appears to apply on its face to Trump and Kushner.
However, experts say the interpretation of the law could allow for Trump to have "wiggle room" should he choose to bring Kushner on board.
The Obama White House has not responded to a request for comment on how it interprets the statute.
PAST EXAMPLES TO CONSIDER
It would hardly be the first time a president has run into issues with nepotism in the White House.
John F. Kennedy picked his brother, Robert Kennedy, as his attorney general, though the current anti-nepotism statute wasn’t passed until 1967 -- four years after JFK was assassinated.
A lobbying group at the time, known as the Association of American Physicians and Surgeons, alleged that Hillary Clinton was acting outside her non-governmental role, and thus both were in violation of anti-nepotism laws.
The court's ruling was that the White House and Executive Office of the President were not agencies under federal anti-nepotism law. Multiple law experts contacted by ABC News believe this made way for the incoming president to potentially have leeway to appoint relatives to advisory positions in the White House.
Due to the 1993 ruling, legal experts say Trump's wiggle room would be if he does not pay Kushner a salary, and appoints him to an advisory board that doesn't fall under a specific government agency.
"I think it clearly violates the intent of the law," said University of Minnesota law professor Richard Painter, who served as a Chief White House Ethics Lawyer from 2005-2007. "But there are arguments that could be used to try and wiggle around it if you were making an appointment in the White House."
Washington University of St. Louis law professor Kathleen Clark said Kushner would very likely still have to sign a non-disclosure agreement and another agreement not to trade on any sensitive information made available to him due to his access to the president.
There would be no technical restrictions on Trump keeping Kushner close as an informal adviser with no official role. And hiring Kushner as a "government contractor" could separate him entirely from the reach of the anti-nepotism statute, the experts argued.
Experts agree the most significant consequences for Trump would likely be political in nature, rather than legal -- at least initially.
Painter noted the public backlash against Hillary Clinton skyrocketed as she carried out her role on the president's health care task force. It resulted in a congressional revolt that sunk the Clintons' health care bill.
Depending on Kushner's role, a legal challenge could take years to bring to court and finally be resolved.
"At a minimum there will be litigation about what the statute means," former Special Counsel to President Obama Norm Eisen told ABC News. "There are legal arguments both ways, but why would you want to have a fight about that?"
In the end it could be Kushner who would face the highest risk if accepted into any kind of government role.
He would then be subject to the conflict of interest laws that Trump does not have to face, and the conflicts posed by his current business holdings could be immense, experts argue.
"If you were to come into government as a government employee, including on one of those presidential commissions, he would be subject to the criminal conflict of interest statute," Painter said. "That's the code that does not apply to the president, which is why the president-elect doesn't really want to sell off his business interests. So does Kushner really want to do this?"
The Office of Special Counsel, which would be in charge of investigating and prosecuting any violation of the anti-nepotism statute, declined comment to ABC News.