A network of trenches at Dreghorn Woods, Colinton, which it is estimated would cost around £10,000 to save, could soon disappear as they become overgrown by trees.
But MoD archaeologist Philip Abramson, who visited the trenches, which were used to train troops before they went to the battlefront, has said they are “not under threat”.
“It is still early days, but the department is looking into securing the necessary funds to carry out survey work to fully assess the site’s extent, condition and historical and archaeological significance.”
The drive to save the trenches, which is being backed by the Evening News, is being led by writer and historian Lynne Gladstone-Millar, whose father, William Ewart Gladstone-Millar, was trained in the trenches before he was sent to the Battle of the Somme.
The 16th Battalion The Royal Scots dug trenches in the Colinton and Dreghorn area, which at that time was countryside, before they made their way to France.
Representatives from Historic Scotland, the MoD and the city council met last month to discuss how the trenches could be preserved. The area of Dreghorn Woods where the trenches lie is open to the public and is owned by the MoD.
Mr Abramson was called in to assess the former training site after concerns were raised about the trenches’ deteriorating state, but he said he found them to be in a “relatively good” condition.
He said: “The system appeared to be fairly extensive, situated on land above the Bonaly Burn and running down the steep slope towards the burn.
“However, because of the woodland it was not possible to establish the full extent of the trench system and its ‘shape’.”
He added the Dreghorn trenches appeared to be in as good a condition as two other examples, at Otterburn in Northumberland and Barry Buddon, Carnoustie. But he added that more work needed to be done to make sure.
Peter Gray, chairman of Colinton Amenity Association, which has joined the campaign said: “Saving the trenches comes down to cash. If the MoD are looking into funding, that’s a good way to take this forward – we have our fingers crossed.”
Ms Gladstone-Millar said: “I’m delighted at things are moving forward, securing the funding to carry out the survey is a vital thing.”