Fenway Sports Group, headed by Liverpool's principal owner John W Henry, was reported to be ready to consider offers for the Barclays Premier League club.
The group completed its purchase of Liverpool in October 2010, after a turbulent period under previous owners George Gillett and Tom Hicks.
Liverpool have been unable to play their way into the Champions League places since the new owners moved in, despite heavy investment in the playing staff, with manager Brendan Rodgers guiding his side to seventh place last season.
The Sun newspaper claims Liverpool is "unofficially" on the market with a price tag of £350million, however Liverpool and their owners state that is not the case.
A club 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."
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."
The Sun reports that Fenway Sports Group received a takeover proposal from Saudi Arabian oil firm Saudi Aramco recently, and states that City banking sources claim two American billionaires could also be potential buyers.