Jordan would be the developer of the housing project if he and city officials can reach an agreement.
Jordan and his legal counsel previously offered to build 450 homes on the site, fewer than what they say is allowed under county rules. On Tuesday, Jordan offered to lower the number of homes to 376.
However, it would be helpful to be able to build 50 to 60 homes per year, "for a project like this to make sense," said Jordan's lawyer, Krista McGowan.
McGowan asked the council to lift sewer restrictions that would limit the project to building 15 to 25 homes per year.
While the site is in the county and subject to county land-use laws, it is subject to the city's annexation policy because the site lies next to the city line and the project would use city water and sewer service.
Residents who live near the site have criticized the plans, saying the impact on local traffic and forestry would be too great.
The proposal has been before the council several times. Most recently, in May, the City Council was set to vote on the proposal but after Councilman Kristin B. Aleshire raised concerns, the council voted to table the annexation.
Councilman Lewis C. Metzner said Tuesday the council faces a deadline on the decision this month. Under state law, he said, if the council does not vote to approve annexation, it could lose its ability to annex.
Metzner said he favored annexation, although he said there are significant problems to work out even if the council agrees to the project, including how the project will fare under the upcoming adequate public facilities ordinance and state-mandated sewer restrictions.
The council likely will take one last look at the agreement next week, and is expected to vote on the matter on June 21.