Klopp has been linked with the Three Lions job after Gareth Southgate left the post last week.
Alexander-Arnold told the Mirror: "I enjoyed every moment I worked with him, we shared amazing memories, forged an amazing relationship, an amazing bond. So of course if that were to happen, we would pick up where we left off.
“I would be surprised if he did take it. It was clear when he announced when he was leaving, the conversations I have had with him, everything on social media, he seems to be enjoying his time off, so it would be a huge surprise.”
He added, "My dream now is to win the World Cup. Everyone involved in the team wants to go that one step further, and with the quality of the squad, that is our mentality now, whoever the manager may be.”