Pretty wet mouthed. Most are not excessively so when they are in "relax" mode, but when enticed by food, after eating or drinking, when panting, etc, then the drool flows.
Beware of any breeder who tells you they have a "dry mouthed" line. It's rubbish.
Hannah leaves a wet puddle by her head when she sleeps. So she lays on a blanket or towel that can be washed. It's icky, but after 15 years with the breed, it doesn't bother me a bit.
Also, be aware that euro danes will be more drooly than the ambred danes.
But yes, unfortunately for those that don't like drool, danes will likely not fit in well for them. I've found slingers on my ceiling fan blades before....