Very difficult if you mean a mouse hover (like viewing a comment).  Easy if
you mean clicking on a cell or using the arrow keys to navigate up & down.

Put the following event macro in the worksheet code area:

Private Sub Worksheet_SelectionChange(ByVal Target As Range)
Set r = Range("A:A")
If Intersect(r, Target) Is Nothing Then Exit Sub
Application.EnableEvents = False
Range("B1").Value = Target.Value
Application.EnableEvents = True
End Sub

You could put some VBA code in your worksheet. Press Alt+F11 to activate
VBA. Select the worksheet name in the workbook where you want the code and
double click on it and paste the following code in the code window.

Private Sub Worksheet_SelectionChange(ByVal Target As Range)
  If Intersect(Target, Range("a:a")) Is Nothing Then Exit Sub
  Range("b1") = Target
End Sub

Then press Alt+F11 to return to your worksheet.

If your cursor is in Column A you will see the value of the cell in Column A
appear in B1