The Enquirer understands that ISG, Willmott Dixon, Galliford Try and Wates have all tendered for the job.
A winner is due shortly before work starts on site by the end of the year and completes in 2012.
Consultant WYG has been appointed by London Borough of Lewisham to provide structural engineering expertise throughout the two year project.
The redevelopment will see the Victorian baths brought back to life with a part demolition and new build offering the latest leisure facilities to the local residents of Forest Hill.
The new leisure centre will keep the existing frontage which will be refurbished to form the main entrance. The new building will include a six lane 25-metre pool, a 16.7 metre learner pool, fitness gym, two studios, a community room and a café.
Tony Driscoll, Regional Director WYG Group said: “This is a technically challenging project with the added constraint of the retained Victorian frontage building, however our civil and structural engineers have been involved in many award-winning projects.”
Councillor Chris Best, Cabinet Member for Community Services, Lewisham Council said: “It has been a real challenge trying to find a design that can accommodate the many different needs of the local community.
“An absolute priority has been to make sure the new facility is fully accessible to everyone who chooses to use it but we have also had to work within tight budget constraints as well as the restrictions placed on us by the size and shape of the site.”
The pool was originally built in 1885 but was closed in 2006 due to health and safety concerns.