Cannot attach asset to monobehaviour field

Questions & Answers
1

I have a button with this component in the scene:

public class BuyButton : MonoBehaviour
{
    [SerializeField]
    private Tower tower;
    // ...
}

Tower looks like this:

public class Tower : MonoBehaviour
{
   // ...
}

In the editor, when editing a button with BuyButton, this allows me to select objects having Tower components in the scene.
But for some reason the picker won’t show me objects having Tower from assets:

175033-unitypickassetwithbehaviour-composited.png
175033-unitypickassetwithbehaviour-composited.png1487×1080 256 KB

Why can’t assets be selected in this picker ? Is this a limitation of unity? how To bypass it ?

I could change the type to gameObject and then get the component in script but that feels rather cumbersome especially when it works properly with objets present in the scene

2

To me it look like a limititation in unity, anyway, just drag and drop the reference of the object instead of clicking in the inspect button

3

Is it because tower is a private field?