All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The scholars stated that the saliva of the meat of animals and birds that we are allowed to eat, is pure with the exception of an animal or a bird that eats impurities. Therefore, if it is permissible to eat the meat of the bird which you referred to in the question, meaning that it does not have claws to hunt with, and it does not eat impurities, then it becomes permissible to prepare food with its nest which it makes with its saliva because its saliva is pure.
In principle all kinds of food are permissible unless there is evidence that a particular kind of food is forbidden.
Some scholars are of the view that it is permissible to eat the meat of a swallow, and that if its nest is soaked in water for one day and night, it becomes beneficial for measles disease.
For more benefit on the ruling of eating the meat of a swallow, please refer to Fatwa 92513.
Allaah Knows best.