Just want to say that, I think jQuery's mouseenter and mouseleave events would make this a lot easier, but if you can't use them, maybe this will help you.
Depending on how your page is laid out, this may not be too difficult.  You can get the position of your element using the following.  Quoting from another answer
element.offsetLeft and element.offsetTop are the pure javascript
  properties for finding an element's position with respect to its
  offsetParent; being the nearest parent element with a position of
  relative or absolute
So, if your element is positioned relatively to the body, so far so good (We don't need to adjust anything).
Now, if we attach an event to the document mousemove event, we can get the current coordinates of the mouse:
document.addEventListener('mousemove', function (e) {
    var x = e.clientX;
    var y = e.clientY;
}, false);
Now we just need to determine if the mouse falls within the element.  To do that we need the height and width of the element.  Quoting from another answer
You should use the .offsetWidth and .offsetHeight properties. Note
  they belong to the element, not .style.
For example:
var element = document.getElementById('element');
var height = element.offsetHeight;
var width = element.offsetWidth;
Now we have all the information we need, and just need to determine if the mouse falls within the element.  We might use something like this:
var onmove = function(e) {
   var minX = element.offsetLeft;
   var maxX = minX + element.offsetWidth;
   var minY = element.offsetTop;
   var maxY = minY + element.offsetHeight;
   if(e.clientX >= minX && e.clientX <= maxX)
       //good horizontally
   if(e.clientY >= minY && e.clientY <= maxY)
       //good vertically
}