Nacro and the Rehabilitation for Addicted Prisoners Trust have teamed up with private security firm G4S and construction company Galliford Try to form a consortium bidding to run Maghull and Belmarsh West prisons.
The charities say they have joined the consortium because it will allow them to have a bigger role in planning and developing services for prisoners.
Paul Cavadino, chief executive of Nacro, said the involvement of drug and rehabilitation charities in the design and development of prison services would ensure that prisons were "providing high quality resettlement and regeneration".
Meanwhile, two other charities – Rainer Crime Concern and Turning Point – are part of another consortium bidding for the Maghull and Belmarsh West contracts.
A Rainer Crime Concern spokeswoman said that if the consortium won the bid the charities would be "involved from the very start in developing the design and specification of prison and support services".
The two bids will be submitted to the Government by October, with a decision on the preferred bidder expected in early 2009.
Stephen Bubb, head of charity chief executives body Acevo, said: "The third sector has a long history of working closely with offenders. Running prisons is the next logical step for the sector and shows that we have the strength to deliver mainstream public services."