Liverpool's owners say they "would consider new shareholders" following reports that the club is up for sale.
FSG said it "remains fully committed to the success of Liverpool, both on and off the pitch".
Liverpool, Premier League runners-up last season, are eighth in the table.
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.