Move object towards mouse but if mouse moves object fallows it's original path

You could always use a Ray coming from the main camera, then use a RaycastHit to determine the new position you want the object to travel to. You would attach a script like this to the object you want to move. This requires that you have some sort of terrain or other collider that you can click on for your object to travel to.

 //Example.cs
 //C-Sharp
 
 using UnityEngine;
 using System.Collections;
 
 public class Example : MonoBehaviour
 {
     Vector3 newPosition;
     Ray ray;
     RaycastHit hit;
 
     void Awake()
     {
         newPosition = transform.position;    
     }
     
     void Update()
     {
         ray = Camera.main.ScreenPointToRay(Input.mousePosition);
         if(Physics.Raycast(ray, out hit) && Input.GetMouseButtonDown (0))
         {
             newPosition = hit.point;
         }
         transform.position = Vector3.MoveTowards(transform.position, newPosition, 5.0f * Time.smoothDeltaTime);
     }
 }