The newspaper reports that computers on Whitehall's secure intranet were first used in 2009 to add the line "Blame Liverpool fans” to the page.
Then in 2012, changes were made from the same source, with the phrase "You’ll never walk alone” changed to "You’ll never walk again" and later "You’ll never w*** alone.”
The phrase "This is Anfield" was also changed to "This is a S***hole."
The Echo says: "The entries were posted from IP addresses used by computers based in government departments including the Department for Culture, Media and Sport, Her Majesty's Treasury and the Office of the Solicitor General."
A spokesperson from the Cabinet Office confirmed they were investigating: "This is a matter that we will treat with the utmost seriousness and are making urgent inquiries. No one should be in any doubt of the government's position regarding the Hillsborough disaster and its support for the families of the 96 victims and all those affected by the tragedy."
The shocking news emerges less than two weeks after the club marked the 25th anniversary of the Hillsborough disaster in which 96 of their fans died during an FA Cup semi-final, one of the darkest days in the history of English football.
The supporters lost their lives in a crush at the Leppings Lane End of Sheffield Wednesday's ground at the start of the match between Liverpool and Nottingham Forest on April 15, 1989.
New inquests into the deaths started last month after a 2012 High Court decision the quashed accidental death verdicts from 21 years ago following an independent inquiry, which had found new evidence and absolved fans of any responsibility.
The tragedy shocked the world and led to a new era of modern stadiums across Britain, with banks of terracing and metal fences around pitches replaced by seating throughout and better security.
The disaster, in which 766 people were injured, is also the subject of two other investigations, with the government setting up a new police probe in 2012. The establishment of the new investigations was a major victory for victims' families, who never accepted the official version of events in which blame was placed on the fans themselves.
The Independent Police Complaints Commission is also looking into allegations arising from the aftermath, and will review allegations surrounding amendments to statements and the actions of police officers.
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