My Maggie went through that for about three weeks or so after I brought her home. The vet said that it was probably her system getting used to the carpet, furniture materials, etc., in my home and in time, it would go away. Sure enough, it did and she was just fine.
If there is a greenish or yellow discharge from either the eyes or nose, take the pup to the vet as that may indicate an infection. Otherwise, if the mucus is white (opaque) or clear, not to worry.
Good luck with the new pup !!!