House Speaker Becky Lockhart said she plans to appoint members to the committee by next week and have them begin their work in August. The Provo Republican hopes to have the panel's initial report by year's end.
The legal counsel hired by the House will work closely with the Legislature's general counsel, John Fellows, and staff attorneys.
"The request allows for a motivated attorney to play an important role in the history of Utah government," Fellows wrote in a letter accompanying the documents. "More importantly, it allows that attorney an opportunity to serve the people of Utah by performing a vital and consequential task."
The request went out to all members of the Utah State Bar, 142 law school deans, 24 Utah law firms, the American Bar Association and the bar associations in Idaho, Arizona, Colorado and Montana. Firms have until July 25 to submit bids on the contract, which is scheduled to be awarded Aug. 9.
"By appointing the special investigative committee, the Utah House seeks facts ... and is not seeking any predetermined result," Fellows wrote. "The Utah House believes that obtaining evidence and receiving testimony under oath will provide the Utah House and the public with the facts that they need to determine whether, or how, to proceed."
Legislative fiscal analysts estimated that the probe could cost $500,000 to $3 million, depending on the scope and the staffing. They estimated that the House would hire at least one full-time attorney, one part-time attorney and a full-time investigator.
As was the case when the lieutenant governor's office sought to hire a special counsel to investigate Swallow's candidate financial forms, the contract requires disclosure of any potential conflicts of interest.
In the case of the House counsel, the bid documents require the disclosure of any political contributions to Swallow or his predecessor, Mark Shurtleff, or their opponents and revealing any legal work done for potential witnesses.
The investigative committee, established in a 69-3 House vote, is the fifth probe into allegations of misconduct that have been leveled against Swallow.
Federal officers have been investigating Swallow since last year and are working in conjunction with the Salt Lake County district attorney and Davis County attorney.
The lieutenant governor's office is expected to announce the appointment of a special counsel next week to see whether Swallow intentionally omitted payments and business interests from his candidate financial disclosure forms.
And two complaints have been filed with the Utah State Bar, alleging that Swallow violated attorney ethical standards.
Swallow is accused of an array of misconduct, including helping a major donor to Shurtleff's campaign try to avoid a federal investigation into his businesses, promises of special treatment for donors and accepting improper gifts.
Swallow has denied wrongdoing.