FSG, which completed a 300 million pounds ($358 million) takeover of Liverpool in 2010, earlier this month responded to reports of a sale by saying it would explore the option of bringing in investors if it was in Liverpool's "best interest".
"We're exploring a sale, but there's no urgency, no time frame for us, and as far as I'm concerned, it's business as usual," Werner told the Boston Globe newspaper.
"One outcome could be our continued stewardship for quite a while."
Head coach Jurgen Klopp (55) said last week a potential change in Liverpool's ownership would not affect his commitment to the club and played down talk of a sale.
Since FSG took over Liverpool, the club won their first Premier League title in the 2019-20 season while they have also reached the Champions League final three times under Klopp, winning the title in 2019.
They are currently sixth in the league with 22 points from 14 games, with the domestic campaign paused for the World Cup in Qatar.
Earlier this year, Russian Roman Abramovich completed the sale of Chelsea to an investment group led by Todd Boehly and Clearlake Capital for 4.25 billion pounds.
