There's actually a neat little trick, borrowing an approach from the alerts drop down that can sort of do this.
It's a bit long winded, for what it is, but it has a nice effect.
Your notice content needs to have a rather strict structure:
<ul style="margin: 0">
<li class="PopupItemLink" style="list-style: none; cursor: pointer;">
This is a link to a thread <a href="index.php?threads/1" class="PopupItemLink">click here</a> to read it.
Any content inside the <li> tag (must have a PopupItemLink class) will be clickable, and the link it will activate is the <a> tag (must also have a PopupItemLink class).
It's not exactly how you want it - only the content inside the <li> tag will be clickable, but that's still likely to be more effective (and easier to use) than just a small link.
You will only be able to have one a.PopupItemLink inside an li.PopupItemLink for this to work.