This will involve building a new school on the same site that is currently shared by the two schools in Grove Park, Kingsbury, which is scheduled to open in 2013.
The successful contractor will be expected to put the finishing touches to the novated design for the building.
The re-build is being largely paid for by the council which has invested £22m into the project, including £8m of government funding awarded to the authority to help improve special educational needs provision in the borough.
PQQ requests need to be in by 31 August.