The firm saw off competition from rival bidder Bouygues, and the appointment is expected to be finalised over the next few days.
A spokesman for Camden Council said: “The council has now finished appraising the two bids for its BSF programme and a recommendation has been made for the appointment of Bam PPP UK as its preferred bidder.
“This has yet to be confirmed the final award of contract will be subject to approval of the final business case by councillors in July.”
Work on the programme, which involves rebuilding three schools and refurbishing a further eight, is expected to start in September 2010.