No, that's okay. Biathletes also salivate at competitions. This may be due to dehydration. Drink a glass of water before running. Watch your breathing, I often get this kind of saliva when my breathing is out of order. If you are out of breath, you need to make 3-4 slow and noisy inhalation-exhalation and switch to a warm-up pace until breathing is restored. It can also happen if you run in a place with strong gas pollution, I noticed in myself when you have to run along the road.
This means rather that the body does not have enough fluids during physical exertion (this is normal), as a result of which the saliva becomes viscous.