The statue of "Little Barry" -- as Obama was known when he lived in the capital in the late 1960s -- stands in central Jakarta's Menteng Park, a short walk from the US president's former elementary school.
Critics say the site should have been used to honour an Indonesian and 55,000 people have joined a page on social networking website Facebook calling for the statue to be removed.
"We've been discussing for the past two weeks what to do with the statue... whether to take it down, move it elsewhere or retain it. We're finding the best solution," Jakarta parks agency official Dwi Bintarto said.
Obama, who was born in Hawaii, lived for four years as a child in Jakarta from 1967 after his divorced mother married an Indonesian.