That route would leave thousands of Palestinians on the Israeli side of the fence.
Palestinian officials immediately condemned the plan as an attempt by Israel to annex territory they claim for a future independent state.
Olmert's office denied a report in the Haaretz newspaper that the prime minister had already approved the new route, saying he had only ordered officials to look into the possibility.
"The prime minister asked to look into the matter and announced that at the end of the necessary examinations the matter will be discussed by the Cabinet," according to the statement, which said no date had been set for a Cabinet discussion.
According to Haaretz, the new route would enclose the Jewish settlements of Naaleh and Nili — home to 1,500 Israelis — on the Israeli side of the barrier. The new route would also enclose roughly 20,000 Palestinians between the barrier and the frontier with Israel.
The report said residents of the two settlements had asked for the new route.
Miri Eisin, a spokeswoman for Olmert, said the Haaretz report was untrue because Olmert "couldn't simply overturn a Cabinet decision" on the original route of the barrier. Construction in the area of the settlements is incomplete.
Israel says the separation barrier, which is about two-thirds complete, is necessary to stop homicide bombers from reaching Israeli population centers. When it is finished, the massive complex of concrete walls, barbed wire and electronic sensors is expected to stretch roughly 425 miles in length.
The Palestinians charge that the barrier, which dips into the West Bank in many areas to include Israeli settlements, is being used by Israel to take land the Palestinians want for a future state.
"The main goal of it is to annex land, and for annexing at least two settlements they are going at least five kilometers deep into the West Bank," Tofakji said.
The Palestinians claim all of the West Bank, which Israel captured in the 1967 Mideast War, as part of a future independent state.
In the past, the Israeli Supreme Court has ordered the government to move the barrier route closer to Israel's pre-1967 frontier. Should the government approve the new route, it would almost certainly be challenged in court.