Praise be to Allah.
After a great deal of research in the books of hadith, we have not come across any hadith with this meaning, and we do not know of any connection in Islamic teachings between remembering Allah (dhikr) and thirst.
But perhaps the questioner is confused about the saheeh hadith that was narrated and classed as hasan by at-Tirmidhi (3375) and Ibn Maajah (3793) from ‘Abdullah ibn Busr, according to which a man said: O Messenger of Allah, The teachings of Islam are overwhelming for me. Tell me of something that I will be able to adhere to. He said: “Always keep your tongue moist with the remembrance of Allah.” Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
This is applicable when fasting and at other times, but it is more important in the case of fasting, although there is no connection between that and fasting or thirst. Rather what is meant by that is that your tongue should always be constantly busy with the remembrance of Allah (dhikr), and not stopping remembering Him until it becomes dry as a result of moving little.
Al-Mubaarakfoori (may Allah have mercy on him) said: That is, it should be fresh (with dhikr), and if you stop remembering Allah (dhikr), you should resume soon after. This means that you should be constantly remembering Allah." (Tuhfat al-Ahwadhi).
Ibn al-Qayyim (may Allah have mercy on him) stated in his book al-Waabil as-Sayyib min al-Kalim at-Tayyib (p. 41) that remembrance of Allah (dhikr) has more than one hundred benefits, then he listed most of them, but he did not say that one of the benefits of remembering Allah is that it reduces or eliminates thirst for one who is fasting.
And Allah knows best.