Liverpool City Council is threatening to take legal action if the Premier League refuses to change the kick-off time of February's Merseyside derby.
Everton's match against Liverpool at Goodison Park on February 7 is due to start at 5:30pm.
Merseyside Police are concerned that the later-than-usual kick-off time will increase the risk of disorder.
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The issue has arisen after the game was moved to be broadcast live on television.