Ghassan al-Khatib, a cabinet minister, said on Wednesday that Israel should move the wall to the Green Line - the 1967 border separating Israel from the West Bank.
Israel has faced international criticism over the original 720km route of the barrier of wire and concrete looping deep into the West Bank.
Israel says it keeps out "suicide bombers", but Palestinians call it "a land grab".
A senior political source said on Wednesday that Sharon had given instructions to the Defence Ministry to alter the route, but any changes would still need government approval.
Sharon's office said the prime minister had asked for the adjustments to reduce friction with Palestinians.
The news came on the eve of a visit by envoys from Israel's main ally the United States, which has criticised the route of
the barrier for taking in Jewish settlement blocs on West Bank land where Palestinians want a state.
"Sharon is trying to make these changes before a visit to Washington," the source said. Sharon is trying to win President George Bush's approval for a plan for separation from the Palestinians if a US-backed peace "road map" remains stalled."
The plan would probably involve setting a new "security line" along the route of the barrier as well as the withdrawal of settlers from the Gaza Strip.
Stone-thrower shot dead
Also on Wednesday, a Palestinian was shot dead when Israeli occupation troops opened fire on stone-throwers in the southern West Bank refugee camp of al-Arrub, Palestinian medical sources said.
Stone-throwers are often
targeted by the Israeli army
The victim, who was in his twenties, was not immediately identified. The al-Arrub refugee camp lies between the southern towns of Bethlehem and Hebron.
An Israeli military source said a Palestinian in the camp had thrown a Molotov cocktail at an Israeli patrol in the area, prompting the troops to open fire.
"They fired at him and identified a hit," she said.
His death raised the overall death toll since the start of the
Palestinian intifada in September 2000 to 3828, including 2874 Palestinians and 886 Israelis.