At Galashiels, the job entails replacing existing building with a new block of 273 bed spaces costing around £13.5m.
The second lot at the Edinburgh campus is worth £12.8m and will involve building 279 bed spaces.
Work will start in January next year with completion set for June 2012.
Deadline for submission of pre-qualification questionnaires is 28 June.
Between 10 and 16 firms will then be shortlisted and invited to tender on 23 August.