A story on Scottish Television website STV stated that it understood employees of Hearts "were informed of the prospect at a meeting on Tuesday morning".
Uncertainty arose over the finances of the team that sit second from bottom in the SPL on Monday night when the entire board of Ukio Banko Investicine Grupe (UBIG), the investment group who own Hearts, resigned from the Lithuanian company.
But Hearts deny such action took place on Tuesday and in a story on the club's website said: "Heart of Midlothian FC vehemently refutes media claims that its staff were told at a meeting that the club could go into administration.
"The report on the Scottish Television website lacks any sort of foundation and is misleading in the extreme. The club can categorically state there was no such meeting and no such message imparted to staff.
"Such erroneous stories cause distress not only to our staff but their families and the club will be taking the strongest action possible against the responsible parties."
A Hearts spokesperson added: "We are sickened and disgusted by such unsubstantiated content. Articles such as this which have no factual basis, show a complete ignorance of the facts and reflect very badly on the profession of journalism.
"It is a straight-forward shameless act to destabilise the club and we will consider applying for legal advice to seek justice and damages for the business."
Vladimir Romanov, who had been the majority owner of the bank Ukio Bankas, which was declared insolvent in February, quit as chairman of UBIG a week ago. He is still the owner of the club.
Club director Sergejus Fedotovas also stepped down from his duties at UBIG.
Hearts were issued with a transfer ban last year because of late wage and bonus payments. Although this was lifted in January, Hearts are still restricted to signing U-21 players until the end of the season with a one-in one-out policy.