desktop-globals-to-clear is a variable defined in `desktop.el'.
Its value is

(kill-ring kill-ring-yank-pointer search-ring search-ring-yank-pointer regexp-search-ring regexp-search-ring-yank-pointer)

List of global variables that `desktop-clear' will clear.
An element may be variable name (a symbol) or a cons cell of the form
(VAR . FORM). Symbols are set to nil and for cons cells VAR is set
to the value obtained by evaluating FORM.

You can customize this variable.

This variable was introduced, or its default value was changed, in version 22.1 of Emacs.