The right-back did not have the best of games in a 2-2 draw against Manchester United.
Van Dijk could be seen yelling at Alexander-Arnold on more than one occasion during the game at Anfield.
United legend Roy Keane stated post-game: "Trent's defending today, my goodness, it was like schoolboy stuff.
"They're talking about him going to Real Madrid, the way he's defending, he's going to Tranmere Rovers after this. He's got to do better."
Van Dijk, referrining to transfer rumours around his teammate, stated post-game: "I am fine with it. Trent has his own people around him, his family and we are there as well.
"He wants to perform in the best way possible like we all do. That is the main focus. In my opinion, maybe ask him, that is the distraction... the game."