The pair slammed the scheduling with Solskjaer unhappy with United being given the early Saturday kick-off this weekend.
Solskjaer called the decision, following a midweek trip to Istanbul in the Champions League, an “absolute joke”.
Klopp agreed with the Norwegian, hitting out after Liverpool’s draw at Manchester City on Sunday.
Sky Sports and BT Sport play a key role in the fixture list as they choose the games they wish to show on their networks.
Though Mail Online report that Solskjaer and Klopp’s comments have been met with bemusement by TV chiefs.
It’s reported that clubs and broadcasters hold regular talks over the timing of fixtures with clubs having to agree to any schedule changes.
And the Mail add that there was a sense from the TV chiefs that Solskjaer’s comments were more an attempt to galvanise his squad rather than genuine annoyance with broadcasters.
It’s reported that networks are bracing themselves for similar criticism over the Christmas period, though there is a feeling that the clubs can’t have it both ways given the amount of money that is put into the league by the broadcasters.
Klopp had said of the scheduling: “We played after the last international break at 12:30 at Everton.
“On the Wednesday night, some of my players were in Peru. Then we played at 12:30 [on Saturday]. These kinds of things should not happen.
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“I understand 100 per cent the needs of television, 100 per cent. It’s completely normal that you play Saturday, it’s the 12:30 which is the killer.
“We have to find solutions because it’s so tough this year. This intensity is really difficult.
“We get it, we want to play football 100 per cent with all we have – we need to play football, it’s great for the people, it’s great for us, everything is fine. But [playing on] Wednesday night and 12:30 [Saturday] should not be allowed.”