"Creating a government-conferred monopoly would diminish innovation, degrade service to market participants and heighten systemic risk," MBA President and CEO Bob Broeksmit said in a blog published Friday, noting that the Obama administration also explored the possibility.

Broeksmit's renewed opposition adds to mixed opinions on the merger concept, which billionaire and legacy GSE investor Bill Ackman and some others have backed as promoting operational efficiencies these advocates say could bolster the public offering that's being actively explored.

"A merger would enable them to achieve huge synergies both in their operations and in the trading price and spreads of their MBS, savings which could be passed along to consumers in the form of reduced mortgage rates," Ackman said in a social media post earlier this year.

Ed Pinto, a former Fannie Mae chief credit officer and senior fellow at the American Enterprise Institute who advocates for a smaller government footprint in housing, also briefly voiced opposition to a GSE merger at a Cato Institute conference on Thursday.

Pinto acknowledged there are arguments for maintaining the GSEs' public ties, but then added, "The only thing worse than having two of them would be having one of them."

Both Fannie Mae and Freddie Mac's oversight agency and Treasury have been holding meetings this week to solicit input on the public offering concept, according to GSE regulator Bill Pulte, who utilizes social media to provide early indications of policy direction.

ICBA also doubled-down on merger opposition

The Independent Community Bankers of America announced on Thursday that it participated in two of those meetings this week and discussed its position on GSE reform, which includes opposition to a merger similar to MBA's and a call to release them from conservatorship.

"ICBA does not support merging the GSEs into one entity. We believe this action would be overly disruptive and would not foster competition in the secondary market and would stifle innovation," the group said.

Pulte has said that a new public offering that's being considered will likely be for some rather than all of the GSEs' shares, and done this year only if President Trump views it as providing maximum value for American taxpayers. Another official said this week it could be near term.

Public offering could happen in 2025: Lutnick

"It could well be a 'this year' thing," Commerce Secretary Howard Lutnick, who is part of GSE reform talks, told CNBC on Sept. 11. Lutnick also spoke about how he survived the 9/11 attacks in 2001, when he worked for a firm trading mortgage-backed securities and other bonds.

Lutnick reinforced statements from other officials indicating another aim of the public offering is to ensure it creates industry efficiencies.

"What we want to do is keep the price of a home mortgage as low as mathematically possible," he said. 

Lutnick said President Trump wants to make sure that "the agencies are powerful, capable and strong," using a plural reference, but he referred to the public offering that President Trump has referred to as The Great American Mortgage Corporation as involving a single company.

A video posted online promoting the corporation refers to both Fannie and Freddie, and there is some consensus among pundits that a pre-existing joint venture the two entities established to promote operations linked to unified trading of their MBS could be what goes public.

Pulte announced earlier that he's reviving a plan to make that JV securitization platform available to the private market and rebranding it as U.S. Financial Technology.

One way the GSEs' footprint could be shrunk

It's unclear whether offering some of the GSEs shares to investors in public offering could reduce their footprint and open up some opportunity for private companies the way some have hoped in previous rounds of reform.

It's unlikely in the administrative approach that appears to be the most likely path but there is one way it could be done, said Norbert Michel, vice president and director of Cato's Center for Monetary and Financial Alternatives.

"I think the most productive avenue to go down is to finally, finally, after all these years having no administration ever doing it, write a rule that addresses the excessive use clause in their charters," he said. "I think that's probably the best hope for minimizing or shrinking them. That, by itself, will be controversial as anything, but you could do that administratively and shrink the company."

Developments affecting existing shares

While there have been references to plans for an initial public offering from the GSEs, some have debated the term given the two entities currently have shares trading. 

"It's not an IPO because there's nothing initial about it, but they're going to do a secondary offering that is going to sell stock in these entities, and then the taxpayer will get the benefit of that in one way or another, I think," David Dworkin, president and CEO of the National Housing Conference and a former Treasury official, said at the Cato Institute event.

The GSEs' existing shares received renewed coverage from B. Riley and a buy recommendation from Deutsche Bank this week.

B. Riley also had been one of the leaders in covering the GSEs' shares during Trump's first term, when there also were proactive efforts to reform them.