The authority closed the bidding process Friday after they collected about 40 inquiries from across the Four Corners, according to Donny Jones, the authority's grant manager. The bidding process started in late April.
The authority will allow a 15-day bid review process before choosing which company to work with.
The authority expects to award a contract in early June.
In March, the authority temporarily took over the project.
The homes, built between 2004 and 2006, were originally constructed by Shiprock Housing, Inc.
They were left after the company encountered financial troubles when one of its subcontractors, Nevada-based Lodgebuilder, went belly up. Lodgebuilder's owner, William Aubrey, had been mismanaging his finances.
A federal jury in Las Vegas, Nev., found Aubrey guilty earlier this month of taking money from the authority and spending it on gambling, furs, jewelry, and thoroughbred horse training, The Associated Press reported.
Chester Carl, a co-defendant and former Navajo Housing Authority executive director, was acquitted.
Though Carl expressed interest in returning to the authority, his return is considered unlikely.
"The impacts of Chester Carl's mismanagement of NHA caused many disruptions and today we are still cleaning up a number of items as a result of his actions and inactions," said Christian Bigwater, authority spokesman. "We had to overcome federal intense scrutiny and dig out from under numerous (U.S. Department of Housing and Urban Development) findings. NHA's issues with Chester Carl are not over yet.
The authority filed a lawsuit against Carl in 2009 for a matter unrelated to the Shiprock housing fiasco, though it has yet to go to court in the Window Rock District Court in Window Rock, Ariz., the Navajo Nation's capital.
Between Aubrey and Carl, several of the authority's development projects were derailed, including the one in Shiprock.
In Shiprock alone, 91 homes were built, and only one has a family living in it. The remaining 90 never reached completion and were severely damaged, if not by vandals and thieves, by the weather. Several of the homes have burned down.
The houses initially cost about $9 million to build, and they are expected to cost more than $9.3 million to level and then rebuild. The new structures will have the exact same layouts as the originals.
Although the authority has not received all of the money it lost because of the Lodgebuilder fallout, an estimated $17 million — according to Bigwater, it is working on getting most of it back.
The authority also is working on reforming its policies so as not to allow similar mismanagement to reoccur and thwart current efforts.
"The actions of the previous NHA administration has moved us to reform the organization to ensure there is accountability, transparency, and tight internal controls to ensure that these events will not occur again at the NHA," Bigwater said.
Jenny Kane can be reached at firstname.lastname@example.org; 505-564-4636. Follow her on Twitter @Jenny_Kane