The possible change comes amid a heated controversy over the so-called over-classification of materials and an FBI probe into whether classified information on Clinton's private email server was mishandled.
In a recent memo, Director of National Intelligence James Clapper asked the heads of the country's intelligence agencies "whether the CONFIDENTIAL classification level can be eliminated" from agency guides as well as "the negative impacts this might have on mission success."
In his memo, Clapper said the change "could promote transparency," specifically noting how the United Kingdom "successfully eliminated CONFIDENTIAL without impact in April 2014."
The classification change isn't expected to take place until after President Barack Obama leaves office, should it happen at all, and wouldn't determine how the State Department and other government departments classify information or otherwise impact the investigation surrounding Clinton.
Currently, Clinton is facing questions over her use of a private email server while secretary.
Some 2,101 of the emails sent on that server that were turned over to the State Department and subsequently released to the public were deemed classified -- and more than 95% of those were at the "confidential" level.
Clinton and State Department officials insist none of the emails were marked as classified when she sent or received them, but her critics argue she put national security information in jeopardy by communicating on the unsecure server -- a charge her campaign officials say is a reflection of "over-classification run amok."
President Barack Obama, defending Clinton in a recent interview with Fox News, said, "There's classified and then there's classified."
Obama's administration has sought to create clearer classification guidelines over the last seven years.
In a 2009 executive order, President Barack Obama ordered all agency heads to review of their classification guidelines on a regular basis, "to ensure the guidance reflects current circumstances and to identify classified information that no longer requires protection and can be declassified."
The next such review is due at the end of June 2017, so Clapper and other agency heads are beginning the process of soliciting guidance.
Officials at the State Department would not comment on whether they are considering eliminating the "confidential" label themselves but said they "will conduct a review of our guidance and provide a final summary of that review to the National Archives in 2017."
It's unclear what impact the classification change would have were it to happen.
"I think the memo does some good things, but the proof is in the pudding," said Nate Jones, director of the Freedom of Information Act (FOIA) Project for the George Washington University National Security Archive.
Jones noted that agencies could merely classify documents they would normally tag as "confidential" with the higher "secret" label.
The technical difference between those two levels is whether the information, if disclosed, would cause "damage" or "serious damage" to national security.
"It's so subjective," said Jones. "What's 'damage?' What's 'serious damage?'"
But Jones is optimistic about another proposal Clapper floated in his memo, which would allow agencies increased discretion to declassify information.
That step, Jones said, could pave the way for the release of information widely known to the public but still considered classified.