Jayananda Warnaweera, the curator overseeing its reconstruction, said conservationists had objected to a new building at the stadium that could obstruct views of Galle's 17th century Dutch Fort, a heritage site.
He added that he was worried about meeting the reconstruction deadline.
"We may not be able to meet the targeted November 15 deadline," Warnaweera told AFP, adding that work had also been slowed by continuous rain.
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The Third Test against England is due to start at the southern coastal city's ground on December 18.
The Galle International Stadium, which sits in the shadow of the huge fort walls, was devastated by the December 2004 Indian ocean tsunami which killed an estimated 31,000 people on the island.
Sri Lanka Cricket recommenced construction of the stadium after an initial government order to move it to another location.
A new three-storey building to house player facilities has irked the Galle Heritage Foundation.
"The view of the Fort will be completely