Fenway, headed by Liverpool owner John W Henry, completed the purchase of the club from fellow Americans George Gillett and Tom Hicks in October 2010.
Despite continued investment in the club, Brendan Rodgers' side have failed to secure a place in the UEFA Champions League and finished seventh in the Premier League last season.
But both the club and Fenway Sports Group have been quick to quash a report in The Sun that the Anfield outfit is unofficially up for sale for around £350m.
The newspaper reports that Saudi Arabian oil firm Saudi Aramco recently attempted to buy the Premier League club and states that City banking sources claim two American billionaires could also be potential buyers.
"Fenway Sports Group has made its position clear, Liverpool Football Club is not for sale. There is no truth in this story," said a club spokesman.
A spokesperson for Fenway Sports Group said: "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."