The Estonian War Museum is waiting for 44 landowners to grant permission before replacing more Soviet monuments with neutral grave markers in Ida-Viru County. The first six have already been installed in the region.
Responses are due on Sunday, Friday's "Aktuaalne kaamera" reported.
Museum director Hellar Lill said letters were sent to municipalities' landowners of other properties after an analysis by the Government Office's work group.
The memorials slated for removal are expected to be relocated this year but the exact timings are unknown.
"I can't say at the moment. We are gathering responses, communicating with owners and working with the National Centre for Defence Investment to draw up a work plan. There are no costs for the owners, they will be borne by the state.," said Lill.
The majority of landowners have given their consent already, but some have not.
The Center Party faction in the eastern town of Sillamäe said one big statue in the city should remain.
Town residents interviewed by "Aktuaalne kaamaera" also said they do not agree with its removal.
"The monument does not disturb anyone. It's been here all my life and there would be a feeling of emptiness without it," said Alina.
"I am against removal. My ancestors fought in World War Two, one was lost, the other survived. If the state decides to remove the pillar, it would be a blow to the memories of the people of Sillamäe," Viktor said.
Almost 1 million has been allocated by the government for removing the Soviet monuments and reburying remains in cemeteries.
The Soviet Union occupied Estonia twice between 1940 and 1991.
Editor: Helen Wright