Liverpool's owners accidental they "would see caller shareholders" pursuing reports that the nine are up for sale.
FSG said it "remains afloat committed to the occurrence of Liverpool, some connected and disconnected the pitch".
Liverpool, Premier League runners-up past season, are eighth successful the table.
They person reached the past 16 of the Champions League, wherever they volition look Real Madrid successful a repetition of past year's final.
An FSG connection read: "There person been a fig of caller changes of ownership and rumours of changes successful ownership astatine Premier League clubs and inevitably we are asked regularly astir Fenway Sports Group's ownership successful Liverpool.
"FSG has often received expressions of involvement from 3rd parties seeking to go shareholders successful Liverpool.
"FSG has said earlier that nether the close presumption and conditions we would see caller shareholders if it was successful the champion interests of Liverpool arsenic a club."
Liverpool supporters' union, Spirit of Shankly, said it hoped fans would beryllium consulted successful immoderate talks involving caller owners of the club.
"We person seen reports contiguous that FSG person enactment Liverpool FC up for sale," it said successful a statement.
"Spirit of Shankly person written to LFC for clarification and volition await a reply earlier making comment. We do, however, expect some the Supporters Board and SOS to beryllium engaged successful immoderate portion of the process truthful that supporters are beforehand and centre of immoderate merchantability and the archetypal thoughts of prospective owners.
"We volition support you updated."
FSG bought Liverpool successful a £300m woody nether its aged sanction New England Sports Ventures.
Basketball prima LeBron James has been a part-owner of Liverpool since 2011 and has a 2% involvement which outgo him £4.7m.
He has since become a insignificant partner successful FSG, which besides owns shot broadside Boston Red Sox.
In March RedBird Capital Partners, a backstage concern firm, bought a involvement successful FSG for astir $735m (£533m).
Liverpool's main proprietor John W Henry apologised to the fans successful April 2021 aft the nine backed retired of a projected European Super League.
Liverpool signed striker Darwin Nunez for £64m, attacking midfielder Fabio Carvalho for £5m and defender Calvin Ramsay for £4.2m this summer.
"From clip to clip I would beryllium acceptable to hazard a spot much but I don't determine that and that's fine," manager Jurgen Klopp said successful August.
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