Reports on Saturday suggested that the American investment company were prepared to pull out of the Premier League, with a Saudi Arabian oil firm believed to be interested in purchasing the Anfield side.
|33/1||Liverpool are 33/1 with BetVictor to win the Premier League
A spokesperson said in a statement released to Press Association Sport: "Fenway Sports Group has made its position clear, Liverpool Football Club is not for sale. There is no truth in this story."
And an FSG spokesperson added: "Like so many rumours in the past about a sale of Liverpool Football Club, there is absolutely no truth in this. We have had no meetings with anyone about a sale, we don't know who the source of the rumour is."
FSG purchased Liverpool from American businessmen Tom Hicks and George Gillett in October 2010 after a fan-led protest movement helped oust the controversial duo.
The Boston-based group have since sacked both Roy Hodgson and Kenny Dalglish, with the latter manager having won the only trophy of their tenure thus far in the form of the 2011-12 League Cup.
FSG have also owned Major League Baseball team the Boston Red Sox since 2002, and oversaw the end of their 82-year wait for a World Series victory in 2004.