Olmert, along with Defense Minister Ehud Barak, support a change to the barrier's route through the West Bank region that would leave nearly 990 additional acres of land east of the fence, The Jerusalem Post reported.
The proposed barrier has been the source of controversy in the Middle East as it encroaches on lands owned by Arab villagers, the newspaper said.
Ma'aleh Adumim is to the east of Jerusalem and has the Palestinian town of Abu Dis to the southwest.
Several residents of the Ma'aleh Adumim villages, Abu Dis and Azariya, have filed legal petitions in opposition of the West Bank barrier. The villagers allege the fence would rob them of legally owned lands and encroach on their freedom.
The Post said the High Court is deliberating on those complaints and will consider the proposal from Olmert and Barak.