Salaams.. Allah (swt) cleary specifies in Surah Taubah verse 60 who is entitled to Zakat funds: Here is the verse in the Quran listing the 8 groups of people eligible to receive Zakat.
"The alms are only for the Fuqara' (the poor), and Al-Masakin (the needy) and those employed to collect (the funds); and to attract the hearts of those who have been inclined (towards Islam); and to free the captives; and for those in debt; and for Allah's Cause, and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allah. And Allah is All-Knower, All-Wise." [Al-Quran 9:60]
Clearly Zakat is levied upon and distributed amongst the Muslims. Only in the 4th group of people entitled to zakat in the verse, "and to attract the hearts of those who have been inclined (towards Islam)" may be non-Muslims where you are trying to win them over to the deen. Not being able to give Zakat to non-Muslims however should not stop anyone from giving sadaqah to non-Muslims as is stated below:
Imaam al-Shaafa'i said: “There is nothing wrong with giving charity to a mushrik as a naafilah (supererogatory) action, but he has no right to charity from the obligatory (zakaah). Allaah praised people who, as He says (interpretation of the meaning): ‘… they give food, inspite of their love for it (or for the love of Him), to the Miskeen (the poor), the orphan, and the captive’ [al-Insaan 76:8].” (Kitaab al-Umm, part 2).
And Allah knows best your brother in Islam