Make character face movement direction

Hello, I have a scene with a non-moving camera which is always looking at my character (rotating). I have the following script for the camera rotation:

 void LateUpdate()
 {
     LookAtPlayer();
 }

 void LookAtPlayer()
 {
     transform.rotation = Quaternion.Slerp(transform.rotation, Quaternion.LookRotation(player.transform.position - transform.position), rotationSpeed * Time.deltaTime);
 }

I'm currently using the following script to achieve character movement. The movement itself is working perfectly fine but my character does not always look at the direction of it's movement and I have no clue how to achieve this behaviour.

 void Update()
 {
     moveHorizontal = Input.GetAxis("Horizontal");
     moveVertical = Input.GetAxis("Vertical");

     Vector3 moveDirection = new Vector3(Camera.main.transform.right.x * moveHorizontal, 0f, Camera.main.transform.forward.z * moveVertical);

     if(moveDirection != Vector3.zero)
     {
         Quaternion newRotation = Quaternion.LookRotation(moveDirection);
         transform.rotation = Quaternion.Slerp(transform.rotation, newRotation, Time.deltaTime * 8);
     }
 }

Can you help me out?