If I understand you correctly you want to rotate an object to 'look at' another object over time. One way to do it is with Quaternion.LookRotation and Quaternion.Slerp:

using UnityEngine;

public class SlerpToLookAt: MonoBehaviour
{
    //values that will be set in the Inspector
    public Transform Target;
    public float RotationSpeed;

    //values for internal use
    private Quaternion _lookRotation;
    private Vector3 _direction;

    // Update is called once per frame
    void Update()
    {
       //find the vector pointing from our position to the target
       _direction = (Target.position - transform.position).normalized;

       //create the rotation we need to be in to look at the target
       _lookRotation = Quaternion.LookRotation(_direction);

       //rotate us over time according to speed until we are in the required rotation
       transform.rotation = Quaternion.Slerp(transform.rotation, _lookRotation, Time.deltaTime * RotationSpeed);
    }
}