The Athletic reported that Fenway Sports Group (FSG), which bought Liverpool in 2010, is “inviting offers”.
FSG said it “remains fully committed to the success of Liverpool, both on and off the pitch”.
Liverpool, runners-up last season, are eighth in the Premier League.
They have reached the last 16 of the Champions League, where they will face Real Madrid in a repeat of last year’s final.
An FSG statement read: “There have been a number of recent changes of ownership and rumours of changes in ownership at Premier League clubs and inevitably we are asked regularly about Fenway Sports Group’s ownership in Liverpool.
“FSG has frequently received expressions of interest from third parties seeking to become shareholders in Liverpool.
“FSG has said before that under the right terms and conditions we would consider new shareholders if it was in the best interests of Liverpool as a club.”
FSG bought Liverpool in a £300m deal under its old name New England Sports Ventures.
Basketball star LeBron James has been a part-owner of Liverpool since 2011 and has a 2% stake which he bought for £4.7m.
He has since become a minor partner in FSG, which also owns baseball side Boston Red Sox.
In March RedBird Capital Partners, a private investment firm, bought a stake in FSG for about $735m (£533m).
Liverpool’s principal owner John W Henry apologised to the club’s fans in April 2021 after the club backed out of a proposed European Super League.
Liverpool signed Darwin Nunez, Fabio Carvalho and Calvin Ramsay this summer.
“From time to time I would be ready to risk a bit more but I don’t decide that and that’s fine,” manager Jurgen Klopp said in August.
Source: BBC