Coraline is a creepy, eerie, and, like you say, "ominous" book. At the start of the book, Neil Gaiman provides many warnings or messages that set up the trouble that Coraline is about to confront.
A literal message comes from Mister Bobo, who's described as "the crazy old man upstairs." I suppose it's not technically accurate to say that the message comes from Mister Bobo. The message, as you probably already know, comes from the mice. Bobo is just the middleman.
The message that the mice pass along via Bobo is D"on't go through the door." While Coraline might not know what this means at first, she will soon. The door is the portal to the other world, with the other mother and the other father.
Obviously, Coraline would have been wise to listen to the message from the mice. It would have spared her a lot of trouble. Yet if she wouldn't have gone through the door, there'd be no book. She also wouldn't have been able to liberate the other children.
Perhaps I should take a second to focus on the messengers themselves. Coraline is receiving this message from mice, which reveals how topsy-turvy Coraline's world is. In the normal world, mice don't tend to communicate like humans. In Coraline's world, they do. Again, that should give Coraline a hint about the strange and scary adventure that she seems fated to embark upon,
If you wanted to discuss less figurative messages, you could talk about how Coraline's busy parents and her black cat provide both Coraline and the reader with a warning about what's to come. Black cats are typically linked to witches, devils, and other sinister things. Bad parents, as the story shows, can also lead to frightening problems.
Further Reading