The decision, which may not be formally released until next month, is the culmination of a bidding process that is believed to have cost the contenders a total of £40m.
Other members of the Skanska team are PFI finance house Innisfree and architect HOK, which has imported designers from the USA.
French contractor Bouygues is thought to have decided to pitch for the scheme after it failed to win PFI hospital projects at Oxford and in Havering, east London, leaving it with a high level of capacity.
The winning bidder is expected to go through 12-15 months of negotiation before the final contract is signed and the project gets on site in late 2004.
Bouygues' consortium includes Nightingale Associates and HLM, assisted by Terry Farrell & Partners.
The contract has proved controversial because it only attracted two bidders, and Department of Health's regulations require three.
A decision between the two consortium was first expected in July. The contract was first let in early 2002.
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