The title-chasing club booked their place in the last four of the Champions League on Tuesday night. Liverpool will take on Villarreal for a place in the final, and the first leg will be staged at Anfield on April 27.
Newcastle United entertain second-placed Liverpool at St James’s Park three days later, and the game has a 12.30pm kick-off time so it can be screened live by BT Sport.
The timing has incensed Klopp, who believes it “disadvantages” his team, which is a point behind Premier League leaders Manchester City with seven games left to play.
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Liverpool’s manager said: “If you want to cause us problems, you send us to 12.30pm at Newcastle. I don’t understand it. I can understand that people want to see a football match between Liverpool and Newcastle, but I don’t see why any team should have an advantage or a disadvantage.
“The league and the broadcaster really have to try at least to help. We’ll see. I haven’t heard anything yet. Nobody from BT contacted me yet. But I’d say common sense would tell you that it's probably the right thing to do to move the game slightly backwards.”
Liverpool beat Benfica 6-4 on aggregate to reach the last four.
Meanwhile, Newcastle are 15th in the Premier League and 10 points above the relegation zone. The club is unbeaten in the league at home this year.