Someone (or someones, until Shal's "claimed" feature is implemented,If you mean "hard at work writing a rejection note" that's the situation I was addressing recently (#24214); editing a message already claims it.
What if instead of actually deleting the message, the member's Delete request operates more like a kind of claim. Approval and Rejection by email would be blocked, and the web Pending list would display a badge indication the member's Deletion request.
If a moderator includes the message in an Action from the list (except Delete), a red-banner could report the Deletion Request (and update the list, which might be showing a stale copy from before the member clicked Delete).
Similarly if the member opens the message from the list: a red banner message indicating the Deletion request. Or if the moderator clicks on any of the buttons (again, except Delete) the red banner to indicate the Deletion request.
As with a moderator claim, I'd let the moderator override the Deletion Request after the red banner has been shown once. Not sure why a mod might do that, but I'm sure someone will find it useful.
If no moderator takes care of the Deletion requested message via the web, it should time out and auto-delete, similar to the case with any pending message that isn't approved or rejected.