Sheikh Muhammad b. Sâlih al-`Uthaymîn
Phlegm and mucous that do not reach the mouth do not cause the fast to break. This is the only opinion expressed on the matter in the (Hanbalî) school of law.
If the phlegm and mucous reach the mouth and then the person swallows it back down, there is disagreement among the scholars regarding whether it breaks the fast.
One opinion is that it does break the fast. They compare swallowing phlegm and mucous to the activities of eating and drinking.
The other opinion is that it does not break the fast. They regard phlegm and mucous to be comparable to saliva. Even if a person gathers saliva in his mouth and swallows it, this will not break his fast.
In a case where the scholars are divided in their opinions, then the matter must be referred back to the Qur’ân and Sunnah. Since we are in doubt about whether ingesting phlegm and mucous invalidates the fast, we must consider that the default assumption in Islamic Law in the absence of other evidence is that it does not do so.
Based on this default assumption, we would say that it does not break the fast.
And Allah knows best.
Source: Islam Today