The Israeli prime minister was referring on Sunday to an illegal settlement of up to 500 Jewish colonists living in heavily fortified compounds among the city's 180,000 Palestinians.
Known as al-Khalil to its majority population, the city is host to Tomb of the Patriarchs, religiously significant to both Muslims and Jews, which Sharon also vowed never to abandon.
"Even if one gives Hebron to the Palestinians, Israel will continue to guard the Tomb of the Patriarchs and the Jewish quarter of the town," Sharon said on Sunday during his weekly cabinet meeting, according to a source close to the premier.
Sharon added Israel would keep control of a corridor linking the area to the major Jewish settlement of Kiryat Arba to ensure "territorial continuity".
All Israeli settlements in the occupied West Bank and Gaza are illegal under international law, though Tel Aviv disputes this.
Hebron (al-Khalil) was the first West Bank town Zionist settlers moved into after the territory was captured by Israel in the 1967 war.
According to the 1995 Taba Agreement, greater Hebron was divided into areas H-1, which covers most of the city, and H-2, which covers 20% of the centre and is home to 20,000 Palestinians and more than 200 permanent Jewish colonists.
Jewish numbers are supplemented by a further 200 supporters who come in the daytime from other settlements in the West Bank.
Under the terms of a 1997 accord, Israel pulled out of 80% of Hebron, but about 1200 Israeli soldiers and policemen still guard the Zionist enclave.