A debarment by HUD would be the highest civil penalty for compliance violations.
Under federal lobbying restrictions, Greene was required to disclose yearly whether PHA was spending money - federal as well as non-federal - to influence members of Congress.
The letter to Greene was copied to his attorney, Thomas A. Bergstrom, a former federal prosecutor who specializes in white-collar defense work.
In an interview, Bergstrom stressed that Greene had not been charged with any crime. He said he had been discussing HUD's concerns over lobbying with the agency for months.
Bergstrom said if any PHA lobbyists were paid with federal money, the amount apparently was minuscule. "How do you know what dollars were there, that federal dollars were used?" he asked.
As to HUD's charge that Greene made false statements on federal lobbying disclosure forms, Bergstrom said HUD would need to "prove that he knew and willfully lied about it."
Greene was terminated from PHA in September 2010 after almost 13 years as head of the nation's fourth-largest public housing agency. During his tenure, he was successful at using public money and raising private capital to replace antiquated public housing projects with new communities.
The main lobbying firm for PHA was the American Continental Group in Washington, the letter said.
American Continental's president, David Urban, has said in interviews he was regularly in contact with Greene about his firm's PHA lobbying work.
The HUD letter makes no allegation that American Continental violated agency regulations. The firm consistently filed required disclosures with Congress stating it was lobbying for PHA, records show.
PHA's new president, Kelvin A. Jeremiah, has said PHA has been doing no lobbying since Greene's departure.
HUD's letter comes nearly nine months after the department's independent inspector general called for sanctions "up to and including debarment." The inspector general also called for HUD to pursue actions against Greene under a federal anti-fraud law.
Since Greene's firing in 2010, the FBI and other federal law enforcement agencies have been investigating PHA's activities under his administration, according to sources and documents that have become public.
As a government-funded agency, PHA is prohibited from using federal money to pay lobbyists. Although lobbying isn't barred outright, public housing agencies must disclose if any money is being used to lobby members of Congress.
The HUD letter said PHA violated those rules on two fronts: Some federal money was being used on lobbying and Greene failed to disclose lobbying activity.
HUD listed more than 30 incidents in which lobbyists working for PHA met with congressional staffers or members, including Sen. Bob Casey (D., Pa.), the late Sen. Arlen Specter, and House representatives from Philadelphia.
In addition to American Continental's work, the letter says attorney Sharon Wilson Geno of Philadelphia's Ballard Spahr law firm performed some lobbying work for PHA. She could not be reached for comment.
PHA's lobbying activities were first reported by The Inquirer in January 2012. Less than two weeks after the newspaper's report, the FBI and the U.S. Attorney's Office sought PHA's lobbying records, PHA records show.