The committee will be asked to agree to progress with the detailed design element of the project, which would include meeting with staff of the school to discuss the requirements needed for individual rooms and spaces.
The local authority has said that the contractors, Robertson Construction Group, would also carry out more detailed work on the pricing of various elements.
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The cost to the council will not be known until the project cost is finalised, while the level of grant funding by Scottish Futures Trust is also to be confirmed, but it is expected to come within the £10.6m budgeted for.
Commenting ahead of the meeting next week, Ken Guild, Convener of Dundee City Council's Policy and Resources Committee, said: "I am pleased that we are able to take forward the next element of our already impressive school construction and improvement programme.
"The quality of school buildings is an important factor in helping our children and young people to make the most of the educational opportunities they have.
"A series of consultation meetings were held with school staff to present designs, respond to questions and seek views and contributions to inform the process. Members of the community were also invited to a drop-in session to view the proposed outline design solution."
The policy and resources committee will meet on Monday 19 May.
(JP/IT)
