The Reds are set to face Newcastle on April 30 in the early kick-off and it could well take place just days after the first leg of a Champions League semi-final against Villarreal.
He told reporters: "Because of the success we had so far we play Saturday against City, but it could have been Aston Villa [in the Premier League]. Then we play United, then we play Everton. Then, if we get through tomorrow, we have a semi-final and BT and the Premier League thought we should have Newcastle away at 12.30.
"The schedule, and how people use the fame in the moment - Liverpool is hot and everyone wants to see them - they couldn't care less, the TV stations. It's just not OK.
"If we play a Champions League semi-final, find me another league in the world and another broadcaster who would put the one team in the semi-finals - it might be two or three English teams - on at 12.30. It's like: 'Throw them a little stick between the legs!' What? What are you doing? Why would you do that? That's why it's so difficult, that's why it never happens, because nobody cares.
"It's unbelievably difficult. We are still in three competitions and we play City; you saw how difficult that was. How could I sit here now and think about other cups? We play Benfica tomorrow and how can I sit here thinking about winning the Champions League? I don't. We just try to squeeze everything out to stay as long in the competition as somehow possible and then be there in the final, hopefully, or in the league to make the last decisive step."
But ex-Crystal Palace owner Simon Jordan holds no sympathy for the 'brilliant' German manager and believes he's acting entitled in his battle with broadcasters.
"The difficulty for me is this is nothing Klopp hasn't said before," he told talkSPORT. "He says it every single time. It's constantly everyone else's fault that fixtures exist.
"What these guys forget, and I'm not fan of the broadcasters at times, is that without the broadcasters paying an obscene amount of money into football at times, there wouldn't be the salaries that Jurgen Klopp gets. There wouldn't be the power in the Premier League.
"So on one hand you have all the upside of this juggernaut, this powerful league, this phenomenal set of financial affairs around this league and all that goes with it - and that has a consequence.
"The broadcasters want their pound of flesh, they want to have what they want to have. But they are only asking for what they have agreed. They have agreed a fixture schedule.
"Did Jurgen Klopp say, back in August when the fixtures came out, 'Hold on a minute here, we're on for a quadruple at the beginning of the season and we could have a [Champions League] semi-final there, and we could have an FA Cup semi-final, and we could have my aunt being my uncle.
"So what I want is to move that fixture from 12:30pm because, don't forget, that all of you other 19 clubs in the Premier League, all of you clubs in Europe, and you clubs in Europe, your sole focus is to help us win a quadruple'?.
"He wants dispensation. Newcastle are playing in a competition and Newcastle have less resources than Liverpool, so Newcastle might be quite happy to play at 12:30pm.
"So, because Liverpool's success has driven them to a position where there fixture list has ultimately put them in an invidious position where they are playing more games in a short space of time. It's less than ideal but then, okay, don't be so successful then. What is it you want?"
And Jordan feels Klopp is too willing to enjoy the ramifications of the Premier League's huge broadcast deals but needs to realise it does come with a consequence.
He added: "Has he got some real-time analysis which says that if this was a Spanish team, this is what they would do? If this was a German team, this is what they would do.
"And then the argument would be, this is the salary of x-amount of managers in the Spanish league, this is the salary of the players.
"What do you want? You want it all as a one-way transaction. That's what football people want. All of it as a one-way transaction. But all of this gets you to where you are. I don't care about how it gets me to where I am, I want that, I'm entitled to that, and I want that as well.
"It just seems to me to be something you have just got to get on with. The luxury of being so brilliant as a manager and having such a brilliant team affords you the opportunity to be slightly conflicted when it comes to fixtures. Get on with it.
"No one is sitting here trying to stop Liverpool winning the quadruple and no one is trying to facilitate Liverpool winning the quadruple.
"Football has a sense of entitlement and the stronger Jurgen Klopp gets the more powerful he gets, the more entitlement in him comes out.
"You can see him challenging broadcasters. You saw him getting his pants pulled down by Des Kelly a year ago when he made some ridiculous observations and Des, for once, used some sensible questioning and put him back on his heels."
He added: "But it doesn't mean that he doesn't have a valid point if you can compare and analyse it against what other people have to endure.
"We should want our best managers to have the best opportunity and he does because he's got a brilliant squad. They go and buy a £45-50million forward, nick him off Tottenham, or prevent Tottenham from getting him, to get the boy [Luis] Diaz, because Liverpool can do that.
"You have to have some of the rough with the smooth, don't you?"
From next season, BT will consider moving 12:30pm games to 7:30pm if it can aid a team playing on the previous Wednesday.
And Jordan reckons if Klopp and other managers feel so strongly about the matter they should lobby for change in a constructive manner.
"Here's a solution to that," he said. "The managers should go to their chief executives and say 'we don't want to play any 12:30pm games'. And they got to the Premier League and say 'we want consider very seriously to exclude the 12:30pm broadcast window because we don't want it for our elite teams, and our elite teams are the reasons why these broadcasters are paying the money'. And the conversation gets upped and it gets pragmatically resolved."