Only way I can think of is to concatenate the worksheet name with the cell reference, as follows:
Dim cell As Range
Dim cellAddress As String
Set cell = ThisWorkbook.Worksheets(1).Cells(1, 1)
cellAddress = cell.Parent.Name & "!" & cell.Address(External:=False)
EDIT:
Modify last line to :
cellAddress = "'" & cell.Parent.Name & "'!" & cell.Address(External:=False)
if you want it to work even if there are spaces or other funny characters in the sheet name.