The six-mile-long circuit has 15 stations, and was last upgraded 30 years ago when it had to be closed down.
The works form part of a much more extensive £290m facelift of stations over the next 30 years, but much of the essential works will be carried out ahead of the 2014 Commonwealth Games.
The tunnel and rail upgrade contract will be worth around £25 and include rail and track bed replacement, repairing tunnel linings and upgrading tunnel pumps and sumps.
Work will start in December and run for three years.
The local transport authority is also considering outsourcing long tern maintenance as part of the tendering exercise, which would be the big longterm prize for bidding firms.
The PQQ is available at Public Contracts Scotland web site at http://www.publiccontractsscotland.gov.uK