The Daily Mail says Klopp has already vented his frustrations at Sky and BT Sport for causing fixture congestion with Liverpool facing a 12.30pm kick-off in Brighton on Saturday, three days after their Champions League defeat by Atalanta.
But now Liverpool's home game with Wolves has been picked for coverage by Sky, meaning they will now play on Sunday, December 6 at 7.15pm.
The Reds then travel to Norway to face FC Midtjylland on Wednesday, December 9 with an early kick-off time of 5.55pm.
Klopp's side will be back in action with a 4.30pm kick-off at Fulham on Sunday, December 13 and then face a quick turnaround for a top-of-the-table clash with Tottenham at Anfield on Wednesday, December 16 - which will kick-off at 8pm.
After that big game, it will be a trip to Selhurst Park for a 12.30pm kick-off against Crystal Palace on Saturday, December 19.
That means Liverpool will play five games in 14 days, with just two of the fixtures at Anfield.