Dave Weigel, writing for Slate, an online publication, first proposed the idea, The Detroit News reported Monday.
Washington Post writer Charles Lane on Sunday repeated the proposal that Snyder give the job to Romney, noting the former GOP presidential candidate 's experience at Bain Capital as a turnaround expert.
Romney is also familiar with Detroit. "He has got the expertise, he's a hometown guy, and he is kind of a political free agent at this point," Lane said.
Snyder has painted a picture of who is is looking for to serve as the turnaround artist for Detroit, which is the largest city to ever have the state move in and declare a fiscal emergency.
"It's a person who has been successful in terms of using interpersonal skills in a very, very challenging situation that involves many different constituencies or different groups," Snyder said.
Snyder said he would also name a person who "has extensive financial and legal backgrounds that doesn't need to get up to speed in terms of the challenges and issues about dealing with long-term liabilities and tax issues or getting up to speed with the facts of this situation. And it's someone who's got a track record of making decisions."
The state said on Feb. 19 that Detroit had a $327 million deficit and $14.9 billion in unfunded pension liabilities.
By declaring Detroit in crisis, the state's next step is to name an emergency manager for the city.
A manager who is decisive and has thick skin would be appropriate for the job, many have said.
Bob Daddow, Oakland County's deputy executive, who served on the financial review teams for Pontiac and Flint and helped craft Public Act 4, says he's not sure who Snyder has in mind for Detroit.
"It's got to be a strong person, someone willing to take criticism, someone with a good restructuring background. They need somebody here who is really special." said Bob Daddow, deputy executive of Michigan's Oakland County.