Sir Robert McAlpine and Taylor Woodrow will submit final plans next month for the 60,000-seat stadium, before detailed planning consent is considered in October.
An Arsenal spokesperson confirmed that the club was talking to two contractors for the two-stage tender, but would not name them.
He said: "Two contractors will submit final bids in September."
There are also plans to turn the present 10.5-acre ground at Highbury into a mixed development with housing and small business units designed by architect Allies & Morrison. Outline planning has been granted for this proposal.
A waste unit, currently on the site of the proposed stadium in Islington, will be demolished. The council then intends to build a new unit elsewhere alongside housing and council offices to be designed by architect CZWG.
There are plans to turn the present ground at Highbury into a mixed development
Andrew Wyllie, managing director of Taylor Woodrow's construction division, said he wanted to find a way to carry out all three developments.
He said Taylor Woodrow could provide the stadium but was also in discussion about the housing projects.
He said: "We are looking to provide a total solution for the stadium and the surrounding area. We could provide the stadium as well as the housing requirements that all three developments demand."
Taylor Woodrow added Bryant Homes to its portfolio earlier this year when it acquired the Bryant Group, giving it greater housing capacity.