Twitter has been searching for ways to make money since Elon Musk took over the social media platform in October.
The new owner had acknowledged that it was losing $4 million a day, and advertisers were fleeing the microblogging platform amid concerns over lax moderation after substantial staff cuts.
And one method to raise revenue that has been under consideration is to put popular usernames up for auction, the New York Times reported.
Mr Musk has previously said that Twitter was preparing to delete 1.5 billion inactive accounts to free up dormant handles or usernames.
It is not known how much certain handles may be worth if they match those of famous brands or people.
It is unclear if the project will move forward, the report said, but discussions have taken place between engineers on running the online auctions.
Twitter's rules prohibit “username squatting”.
“Please note that if an account has had no updates, no profile image, and there is no intent to mislead, it typically means there's no name-squatting or impersonation,” Twitter's rules state.
“Note that we will not release squatted usernames except in cases of trademark infringement.
“Attempts to sell, buy or solicit other forms of payment in exchange for usernames are also violations and may result in permanent account suspension.”
Twitter is also auctioning off a host of items from its San Francisco headquarters.
The auction includes kitchen equipment such as coffee machines, ovens, grills and griddles, braising pans and a rotisserie.
Electronics are also on sale, with projectors, Google tablets and Apple computers and monitors listed.
Chairs and soft furnishings, a blue Twitter statue and an @ sculpture planter are among the 265 items.
Opening bids start at either $25 or $50, with the Heritage Global Partners auction opening on January 17 and closing the following day.
“Twitter has had a massive drop in revenue, due to activist groups pressuring advertisers, even though nothing has changed with content moderation and we did everything we could to appease the activists,” Mr Musk said in a tweet on November 4.
Since his acquisition, Mr Musk launched the Twitter Blue subscription service, which allows subscribers to edit tweets, upload 1080p videos and get a blue tick account verification in exchange for a monthly fee.
Mr Musk said last month that he would resign as Twitter chief executive once he found someone “foolish enough to take the job”.
The billionaire made the announcement on the social media platform after promising to abide by the result of a 12-hour Twitter poll.
Previously the world's richest person, he has seen his wealth fall at a record-setting pace recently and became the first person in the world to lose more than $200 billion.
He has been surpassed by Bernard Arnault, owner of luxury goods group LVMH, as the world's richest.