Your question is unclear, you want to store the object that triggers the OnTriggerEnter?

EDITED in response to feedback

GameObject kObject;

void OnTriggerEnter(Collider collider)
{
    kObject = collider.gameObject.GetComponent<ComponentType>().variable;
}

the variable "gameObject" of MonoBehaviour is always the GameObject to which the script is attached - afaik, you can't change it. From what I understand, you want to "reassign" a script from one GameObject to another. Well, I don't think you can do that. I would recommend instead making a "copy constructor" of sorts in the script you are trying to reassign, that would take as an argument a GameObject, add a copy of itself with AddComponent(), and then set all the local vars to their proper values (if you need this). Then call Destroy(this) to destroy the original script. Call this method in your OnEnterTrigger().

Example:

//This class keeps track of the time it exists as it is passed around objects.
public class TimeBaton : MonoBehaviour {

    public float time = 0;

    void Update() {
        time += Time.deltaTime;
    }

    //Call this method when the baton is passed from one object to another
    public void BatonPass(GameObject go) {
        //create new instance
        TimeBaton child = go.AddComponent<TimeBaton>();
        //copy var
        child.time = this.time;
        //destroy original
        Destroy(this);
    }
}