If you want to use a manager, you should use the PopUpManager for this, but my own opinion is that would probably be overkill.
If you're using MXML, you could try adding the notification element to your page, positioned the way you want. Once you're happy with that, set its visible attribute to false. Then add event listeners to the appropriate events to change the value of the element's visible property.
If you're using ActionScript, I would create a 'Notification' class to define the appearance and any functionality of the notification element. I might subclass Canvas to do this, though subclassing Sprite may give you all the functionality you would need. Once you have a Notification object, you can add event listeners to the appropriate events to create/position the notification element or destroy it.