Coutinho is believed to have handed in a transfer request on Friday, amid growing links with La Liga giants Barca, who are looking to fill the void left by Neymar.
The Brazil international's request came just hours after Liverpool insisted they will not entertain any offers for the 25-year-old.
Coutinho, who missed Saturday's season-opening 3-3 draw at Watford in the Premier League, will sit out the first leg of Liverpool's Champions League play-off against Hoffenheim on Tuesday due to a back problem.
As doubts remain over Coutinho, Liverpool manager Klopp admitted his hands are tied.
"If, for example, there is an offer for a player and I say, 'No', and the owners say, 'Yes, let's ask for a number on how much they want to pay'. And I say, 'I don't want to hear it'. But they say, 'We want to hear it, £50million … £50 million is cool,'" Klopp said. "So then they sell the player — that is how a club works.
"That is how it was with Hans-Joachim Watzke [chief executive] at Dortmund. Do you think I said, 'Sell Nuri Sahin to Real Madrid as quick as possible?' It was not my decision. The player had a contract. They agreed. I am 100 per cent, really, 100 per cent [when I say] I don't ask for things I can't get and I respect the rules in the game.
"If they [FSG] say they [Barcelona] will bid whatever and we don't want it then it is a clear message. We don't want money, we want to invest in the team and have the best team because we have aims and dreams. That is the message.
"It's not important what I think. I have the player from August 31 latest, again, or when the back issue is sorted," Klopp added. "There is nothing else I can say about it. I think I said, 'I have bosses', right? I have many bosses, including my wife. I can live with this, it's no problem. They [the owners] are 100 per cent clear on it. There is nothing else to say."