Musannaf Ibn Abi Shaybah

Ibrahim has permitted chewing gum while fasting, provided that it does not go down the throat.

Hazrat Aamir says that there is no harm in chewing gum while fasting, provided that one does not swallow the saliva.

Hazrat Mujahid states that Hazrat Aisha (may Allah be pleased with her) considered chewing gum to be impermissible while fasting, but she allowed (chewing) qar (a substance similar to tar or something chewable like it).

Hazrat Ata says that it is permissible to chew gum while fasting, provided that its saliva is not swallowed.