Liverpool owner John Henry says he is not selling the Premier League club, but does expect some investment.
FSG chairman Tom Werner later said the club's owners were "exploring a sale" but could continue their "stewardship for quite a while".
"Are talking with investors about LFC? Yes. Will something happen there? I believe so, but it won't be a sale."
The American was speaking in a question-and-answer session conducted over email.
FSG has been open to investment in Liverpool for several years, and has recently engaged Morgan Stanley and Goldman Sachs in that process.