Attempt 2 at:

views/widget/root_view.h

Index: views/widget/root_view.h
diff --git a/views/widget/root_view.h b/views/widget/root_view.h
index 05887e181a6842565830bfdb215243a61fef1b50..ba1d5d22753a2a0ed5ba2a98deba3c9c925dc50b 100644
--- a/views/widget/root_view.h
+++ b/views/widget/root_view.h
@@ -5,6 +5,7 @@
 #ifndef VIEWS_WIDGET_ROOT_VIEW_H_
 #define VIEWS_WIDGET_ROOT_VIEW_H_
 
+#include <set>
 #include <string>
 
 #include "base/ref_counted.h"
@@ -217,6 +218,10 @@ class RootView : public View,
   void RegisterViewForVisibleBoundsNotification(View* view);
   void UnregisterViewForVisibleBoundsNotification(View* view);
 
+  // Registers/unregisters the View for mouse near events.
+  void RegisterViewForNearNotification(View* view);
+  void UnregisterViewForNearNotification(View* view);
+
   // Returns the next focusable view or view containing a FocusTraversable (NULL
   // if none was found), starting at the starting_view.
   // check_starting_view, can_go_up and can_go_down controls the traversal of
@@ -258,6 +263,15 @@ class RootView : public View,
   // Sets the current cursor, or resets it to the last one if NULL is provided.
   void SetActiveCursor(gfx::NativeCursor cursor);
 
+  // Returns in |near_views| the set of views registered for mouse near events
+  // that overlap with the location of the specified event.
+  void GetViewsRegisteredForNearNotification(const MouseEvent& e,
+                                             std::set<View*>* near_views);
+
+  // Sends OnMouseExitedNear to the set of views the mouse is near and empties
+  // the set.
+  void SendMouseExitedNear();
+
   // The view currently handing down - drag - up
   View* mouse_pressed_handler_;
 
@@ -330,6 +344,16 @@ class RootView : public View,
   bool is_processing_paint_;
 #endif
 
+  // Set of views registered for mouse near events.
+  // NOTE: because views registered for near mouse events can overlap other
+  // views and extend outside the bounds of themselves and ancestors we store
+  // the registered views here and treat them separately. This is generally ok
+  // as there are a small set of views registered for near notification.
+  std::set<View*> registered_near_views_;
+
+  // Set of views the mouse is currently near.
+  std::set<View*> near_views_;
+
   DISALLOW_COPY_AND_ASSIGN(RootView);
 };