Sources close to the project said the military training centre build is running behind schedule due to ground contamination.
And the Enquirer understands that the area hit by possible asbestos contamination is the size of three rugby pitches.
Specialist contractors are currently working on site to deal with the problem.
A Skanska spokesperson said: “Skanska carried out comprehensive asbestos investigations on the Worthy Down site at the beginning of the project.
“Trace amounts were found in soils where construction or demolition had previously taken place, which do not pose a risk to workers, site personnel or visitors.
“The programme was revised to enable work to continue and the base to remain operational.
“Collaboration with the client, the Ministry of Defence, the local authority, the Environmental Health department and the contaminated land officer has been positive and is ongoing.
“As a responsible contractor, Skanska is excavating the contaminated soil in accordance with environmental best practice.
“Those directly involved with the removal process wear full protective clothing, although the fibres do not pose a risk, due to the type and low levels of contamination and the control measures in place.
“No additional precautions are required and the affected working areas are clearly signposted.”
Work started on the site last November to build a new military training centre to replace the Deepcut barracks in Wiltshire.
The scheme – known as Project Wellesley – will take around five years to complete and Skanska beat Lendlease and Vinci to take the job.
The plan is for the centre to be up and running by late 2018, while maintaining training at the site throughout the construction period.
A source close to the project told the Enquirer: “The asbestos levels have taken everyone by surprise and led to huge remediation works with a knock-on effect on the work schedule.”