This exact thing happened to Uni a few weeks back! And the DAY AFTER HER BATH! She waits for us to get ready to go to work on the back of our sofa. She was shaking and hiding her face like she didn't want me to see her gross saliva face. I cleaned her up but it just kept coming back. I had to put a bandana around her neck to catch the drool, like a bib, LOL.
After three days it didn't go away so i took her to the vet. She was eating, playing, pooping everything just fine. He said she most likely licked something slightly toxic to cause the mouth to salivate more to try to get it out, but not toxic enough to actually make her sick. Now that i think about it, we had thai curry noodles the night before, and one noodle fell on the ground. She could have eaten or licked it, in which there was onions and garlic in the noodles!
The vet said if she's acting normally, just wait for it to pass. He said no meds bc we didn't know what it was that she licked. Well the very next day she had a slightly mucous-y poop, and after that the drooly mouth was gone!
Maybe your pup licked something? Pups aren't very picky about what they lick or put into their mouths. When Uni was teething she did not slobber like this so perhaps your pup did lick something?

If he's fine otherwise just wait it out. I know it will seem like forever with the constant wiping! Uni's lasted about 4 days.