The Austrian striker, who the former Borussia Dortmund manager knows well from Arnautovic's time in the Bundesliga with Werder Bremen, has scored seven league goals this season to help Stoke into a mid-table position.
"Arnautovic was young player in Germany who had some problems but he has a big talent. He's scoring goals, making runs behind lines," Klopp told a news conference on Monday.
Klopp has been impressed by Stoke's recent displays, which have included home wins over Manchester City and Manchester United.
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"We know about the quality of Stoke, of course," he said. "It's the team I know most about because I know most of the players.
"This cup is important. We have to go for it. Our target is to win it. It will be tough because Mark Hughes has done a brilliant job."
Klopp was fuming after Liverpool's 2-0 Premier League defeat at West Ham United on Saturday in which he accused his players of not giving 100 percent.
"You have to react to defeats in the right way," he said.
"We were passive. That's not good in life or in football. We have to be more aggressive."
Klopp believes Liverpool have shown vulnerability at defending crosses with goalkeeper Simon Mignolet appearing shaky.
"We have issues with crosses. Before that we had issues with set-pieces. We need to solve that. We've been clear with the words," he added.
Mignolet has come under-fire for a number of mistakes but Klopp dismissed speculation linking the club with Barcelona goalkeeper Marc-Andre ter Stegen.
"Our goalkeeper situation is absolutely okay," he said. "Simon Mignolet is a really good goalkeeper."
Injury-plagued striker Daniel Sturridge is still not available as he continues his recovery from a hamstring injury.
Sturridge has made just a handful of appearances this season and has not featured since early December.
"Daniel has had some little problems. When he's had a row of sessions, I will pick him," Klopp said. "We have to be patient."
Captain Jordan Henderson, sidelined since August after breaking his foot in training, will not be rushed back.
"We have to wait. What's happened with the tendon is painful. There is blood around heel. We can't rush it."
(Reporting by Justin Palmer)
