Hybridizing these two species is a bad idea... we don't know the genetic deformities that could be caused initially or further down the line.. just keep it to the same species. There's no reason not to. Plus, I doubt they would breed successfully anyway, or it would have happened already.
ASF's and mice will foster each others young and raise them as their own. If they grow up in such a way, they will be fine living in the same area.
However, putting an adult ASF in with an adult mouse will likely lead to blood and misfortune, and it's not a good idea. It's a big risk to take.