Bird nests and dryer vents don't mix. It's best to prevent birds from entering your dryer vent. You can do this with a simple cover called a bird guard that fits over your dryer exhaust.
A bird nest can completely clog your dryer vent leading to very long drying times, damage to dryer components and if neglected can be a real fire hazard.
Be warned however, bird guards themselves can clog up with lint. It's very important that if you do have a bird guard over your dryer vent that you monitor and clean it on a regular basis.