The PFI project has a capital value of £17m and a preferred bidder will be announced by mid-December.
A spokesperson for the local authority's department for education and culture said: "The bidders came in to give detailed presentations last week, and they were evaluated against our bidding criteria."
The 25-year contract will include the design of the building facilities management services, such as buildings maintenance, caretaking and security.
Library services will remain the responsibility of the council.
The library, which includes a "life-long learning centre", is the second phase of Oldham's cultural quarter regeneration project. The library will be next to the site of the first phase, the Gallery Oldham, which opened in 2002.
Libraries are politically neutral spaces
Richard Lambert, Oldham council
Libraries are currently being hailed as civic centres for the 21st century. A recent report by architecture watchdog Cabe said that with cafes and lounge areas they would be help to knit together divided communities.
Richard Lambert, head of libraries, information and archives at Oldham council, told Building two months ago that the scheme would help alleviate local disputes.
He said: "Libraries are useful in the situation we have here, because they are seen as neutral spaces, with no political agenda.