Yes, there is a way. Use the worksheet  SelectionChange Event. Within the
VBE go to the worksheet in question, for example  Sheet1. In the drop
down box above the VBE environment, where it normally says "General",
select "Worksheet". In the drop down box to the right select
"SelectionChange".

Or just copy and paste this into the Sheet Module.
Private Sub Worksheet_SelectionChange(ByVal Target As Range)

The "Target" value grabs anything the user  clicks on, within a cell  that
is. So now something like this...

Dim sHold as Variant
sHold = Target.Value

...will grab what's in the cell before you change  it.