The La Liga giants' interest in taking Coutinho to Spain has intensified since Neymar left the Nou Camp for Paris St-Germain last week.
Questioned on whether his job now was to keep Coutinho happy, Klopp added: "I can't keep players happy".
Philippe Coutinho has today sent Liverpool fans into hysteria by handing in a transfer request.
Liverpool stood firm in its stance and also rejected the second bid of £90.4 million.
Midfielder Adam Lallana has been ruled out for three months already, and while they won't be gone for almost as long as he is, Nathaniel Clyne, Daniel Sturridge, and Philippe Coutinho will be joining him on the sidelines for at least the season opener against Watford on Saturday.
Sky Sports claim Coutinho has responded to FSG's statement by telling Liverpool that he wants to leave.More news: Rogers Cup: Denis Shapovalov can't get Penny Oleksiak to play tennis
Philippe Coutinho has rocked Liverpool by handing in a transfer request on the eve of the new season.
Despite looking elsewhere, there is certainly unfinished business between Barcelona, Liverpool and Coutinho in this transfer window, and this afternoon's news will improve the likelihood of them securing the signature of their number one transfer target.
Coutinho will be out of action this weekend when Liverpool begin their Premier League campaign against Watford due to a back injury.
FSG's public stance is likely to encourage Barca to turn its attention towards signing Ousmane Dembele from Borussia Dortmund.
Instead, they had upped the ante less than 24 hours before their Premier League opener against Watford, a game for which manager Juergen Klopp said the Brazilian was injured. It's just that Phil is not available at the moment and, for me, actually the bigger issue is that he is unable to play.
After all, the attacking midfielder only cost the Reds £8.5m back in January 2013.