Modern browsers do away with the classic status bar and instead draw a small tooltip at the bottom of their windows that displays the link target on hover/f
The tooltip provides an indication to the user where a link will take them if clicked. It's part of the standard browser user experience and will be expected by users of your site. Changing this expectation because you don't think it looks nice will probably lead to a poor user experience. Any content shown in that area will be visible as soon as the user stops hovering over a link tag.
I know that any link that doesn't tell me where it is going looks pretty suspicious to me.