The Austrian has seven goals and three assists in his last nine Premier League appearances for the Hammers. Van Dijk has led the Reds to back-to-back clean sheets in their last two matches in all competitions.
Something will have to give at Anfield, but Arnautovic has no fear of the January signing from Southampton.
“I have respect for every opponent, every defender and every team, but I’m not afraid of anyone and I’m not afraid to take them on and to make things happen," he told West Ham's official website. "I’m fit and I will do my best like I always do.
“I played at Anfield twice when I was with Stoke and it’s a hard place to go. But I think we have also done well in the last few games and you can always make something happen. We know football can be crazy."