The Well of Zamzam is a blessing from Allah to Hajar and her son Isma`il. Allah rescued them from thirst and starvation through this well. It gushed forth from the earth beside [the future site of] Al-Haram which was afterwards built by prophet Ibrahim (peace and blessings be upon him) along with his son Isma`il for whom the well flowed. The Well of Zamzam was the main reason that Makkah, the Sacred Town, later become inhabited. It is not reprehensible to purify oneself with Zamzam water.
Imam An-Nawawi said in his book of Fatwas titled “Al-Masa’il Al-Manthurah”, that:
It is not reprehensible “makruh” to purify oneself with Zamzam water according to our opinion. This is the opinion of all the scholars, apart from Ahmad according to one report narrated from him. Our evidence is that there is no sound report that has been narrated to indicate that it is prohibited, and it was reported that the Prophet (peace and blessings be upon him) said: “Water is purifying and nothing makes it impure.”
As for the report that Al-`Abbas said it was forbidden to perform ghusl with the water of Zamzam, this is not a sound report.