In a statement released on the club's official website, FSG said Coutinho would remain a member of the Liverpool squad when the transfer window shuts on 31 August.
It comes two days after the Reds turned down a €100m (£90m) offer from Barcelona for the Brazil international.
The Catalan giants want to sign Coutinho as a replacement for Neymar, who joined Paris Saint-Germain in a world-record £198m move earlier this month.
"The club's definitive stance is that no offers for Philippe will be considered and he will remain a member of Liverpool Football Club when the summer window closes," FSG said.
Manager Jurgen Klopp said on 10 August that Liverpool remained committed to retaining their best players and that no bids for Coutinho would be accepted.
"Liverpool is not a club that has to sell players. That is set in stone. So what they offer in the end doesn't matter," the German was quoted as saying by the Guardian.
"From a financial standpoint, there is no price limit to let him go. No price at which we are ready to give in. Our goal is to have the best possible team. So we want to keep our guys and add new ones. That is our plan."
Coutinho scored 13 goals in 31 league appearances for Liverpool last season to help the club qualify for the Champions League.
His form was rewarded with a new long-term contract worth around £150,000 per week in January, making him the highest paid player at Anfield.
"Today, no player on the planet is unsellable," Klopp said. "But a transfer is also a question of timing and if you have the opportunity and the need to react to such a transfer.
"Also you have to ask, if you have the time to react. But just because of one request of one club, we don't have to think about that. We are not in that situation."