No you can't.
All you can do is
Object source = event.getSource();
if(source == panel) {
//event fired by specific panel
}
But this only makes sense if you have multiple event sources for a single method, e.g.
@UiHandler({"panel1", "panel2"})
void onMouseOver(MouseOverEvent event) {
//dispatch event source here.
}
The above code is pretty much the same as
MouseOverHandler handler = new MouseOverHandler() { //implement... }
panel1.addMouseOverHandler(handler);
panel2.addMouseOverHandler(handler);
-- J.