Answer:
Yes, there is that possibility, but in extremely small proportions. The virus that is used to make the vaccines is reproduced in chicken eggs and then removed and added to the other ingredients. Although there is a purification process employed before the vaccine is completely prepared, there is a potential for some egg or chicken protein residue to remain in the vaccines. For this reason, those who have an allergy to eggs or chicken protein are advised not to take the vaccines. This is true for both the injectible and the nasal spray vaccines. There is no additional animal tissue, blood, or blood by-products in the vaccines, other than that from the initial reproduction process using eggs.
See the related questions below for more information about the vaccine ingredients.