The construction of the barrier along the border which the UN recognises but Lebanon disputes, would divide the Israeli-controlled town of Ghajar in half, requiring most of the 2000 residents to move to the southern side, town residents said.
The town of Alawite Arabs - the Muslim sect Bashar al-Assad, the Syrian president, belongs to - was captured from Syria along with the Golan Heights in the 1967 Middle East war and residents were granted Israeli citizenship.
The border with Lebanon, redrawn by the United Nations after Israel withdrew from south Lebanon in 2000, runs right through the town.
Although residents of the farming community can move freely within its limits, the town is surrounded by mine fields, Israeli army checkpoints at its southern entrance and bases of the Hizb Allah militia on its northern outskirts.
Ghajar has been the frequent target of Lebanese militias, most recently last month when Israeli soldiers and fighters exchanged heavy gunfire in the town.
According to the Shin Bet proposal, residents forced to move south of the wall would be compensated with property on the Israeli side.
But most Ghajar residents oppose the idea, saying Israel must negotiate with the United Nations for the border to go around the town, not through it.
Residents have threatened court action to stop the building of the barrier.
"We will not leave our homes except in coffins"
"We are stuck between a rock and a hard place," Najib Khatib, a member of Ghajar's municipal council, told Israel Radio on Tuesday. "We cannot just be up and moved."
Hundreds of Ghajar residents on Tuesday protested the idea, marching in the city with banners reading "No to division, we will remain united".
In a statement, the residents said: "We will not leave our homes except in coffins."
Army against wall
Ariel Sharon, the Israeli prime minister, will decide on the matter in a meeting on Wednesday with senior security officials, his office said.
Israeli media reported that Sharon is leaning towards opposing the wall.
Israel's military largely opposes the wall, viewing it as capitulation to fighters which will only lead to attacks intensifying, said Amos Malka, the former head of military intelligence.
The village is located in a strategically important place for Israel, tucked between three tributaries to the Jordan river, which serves as a major source for Israeli drinking water.
All but 200 residents of the village fled to Syria during fighting in 1967, when their farmland was captured by Israel. The residents returned to their land shortly after the war.