Three organisations have been invited to submit final tenders to be considered to take over Croydon and Wandsworth's library services.
The decision to offer the opportunity to an external company was made because both authorities have to make significant financial savings over the next few years.
Outsourcing was seen as the best option to reduce costs, while ensuring no library branches would have to close.
Greenwich Leisure Ltd, John Laing Services Ltd and an in-house team from the current Wandsworth library service are now in the process of putting together their final submissions for the eight year contract.
This part of the tendering process follows months of discussions which have allowed both councils to make sure the organisations who submit final bids are all fully capable of running the service.
Bidders were also able to gain a full understanding of both Croydon and Wandsworth's requirements, enabling them to ensure their bid submissions covered all of the essential points.
Councillor Tim Pollard, cabinet member for children, families and learners, said: "This is an important milestone in the project as we have now closed our preliminary discussions with the bidders and they now have three weeks within which to complete and return their tender documents for us to evaluate against established criteria.
"We are confident the result of the process will be a solution that meets the objectives set for us by the many residents who took part in our consultation last year and who told us with resounding clarity they did not want to see any library closures."
The bids are being made for two separate contracts, one with each borough.
A decision on who has been successful is expected to be made in November, with the winning bidder likely to take over the running of the services by April 2013.