Reference: Fataawa Ramadhaan – Volume 2, Page 526, Fatwa No.494;
Majmoo’ Fataawa Samaahatu ash-Shaykh ‘Abdul-‘Azeez bin ‘Adbullaah bin Baaz – Volume 3, Page 251
Question: What is the ruling regarding swallowing saliva whilst fasting?
Response: There is no harm in swallowing saliva and I do not know of any difference of opinion between the people of knowledge if it is out of difficulty or inability to get rid of it.
As for phlegm and sputum, then it must be spat out if it reaches the mouth. It is not permissible to swallow it if the possibility of getting rid of it [exists]; And it is not regarded as similar to saliva.
And with Allaah lies all success.