"These places are threatened with destruction. There have been attacks on the buffer zones around these sites and we don't know what will happen in the future," he said.
The World Heritage Committee will "probably" make a decision on the matter when it meets later in September, according to Eloundou, who says the sites are "demonstrably in danger".
The centre of the Ukrainian port city of Odessa is already on the List of World Heritage in Danger. Several of the city's buildings were destroyed in late July in a Russian attack described by UNESCO as "shameless".
Earlier in July, another historic building was hit in Lviv. According to UNESCO, it was the first time that Russia carried out an attack on an area protected by the World Heritage Convention.
UNESCO has recorded around 270 damages at culturally significant sites across Ukraine since Russia launched its large-scale war of invasion on February 24, 2022.