Answered by Shaykh Amjad Rasheed
Is it permissible for one fasting to chew on gum?
If a substance separates from the gum such that it mixes with the saliva and reaches the body cavity, then it is haram and it invalidates the fast.
However, if it is merely chewing it and no substances reaches the body cavity, then it is permissible but disliked, because it makes one thirsty, and because some have said that it invalidates the fast, as it was indicated in the Tuhfa of Ibn Hajar, (3:425).
Amjad Rasheed
[Translated by Sr. Shazia Ahmad]