The Wall Street Journal says the penalty could be as high as $495,0000.
The fine would be Stern's second in the past month. The earlier one was for $27,000.
People familiar with the matter tell the Journal that the Federal Communications Commission is expected to levy the fine for a Stern show Clear Channel aired last year. That show was the target of a listener's complaint.
Details of the fine were still being finalized late Wednesday and could change, but the statute of limitations for responding to the complaint was to expire Thursday.
"It means that the FCC is finally getting serious," applauded Brent Bozell, president of the Parents Television Council, a conservative religious interest group. "So long as shock jocks abuse the public airwaves, I hope there will be more of this.
"The overwhelming majority of the public that is fed up with its airwaves being abused is finally getting some relief," he told CBS Radio News.
In February, Clear Channel yanked Stern off of six of its stations that had aired the program.
"He's off the air [at Clear Channel] until we get assurances that his programs are going to be in compliance with FCC rules," Executive Vice President Andy Levin told the Journal.
Stern is an employee of Viacom's Infinity Broadcasting unit which syndicates the show and airs it on 18 of its stations. CBSNews.com is also a part of Viacom.
"With the new legislation that's making its way through Congress and which the administration is supporting, these fines are going to become really serious, and even a $27 billion corporation like Viacom is going to feel them," said Bozell.
Stern is on vacation this week, and his agent had no comment. Infinity also had no comment.
However, in recent weeks, in response to the latest indecency crackdown, Stern has lashed out almost daily at other broadcasters, the FCC and the Bush administration.
"My days here are numbered because I dared to speak out against the Bush administration and say that the religious agenda of George W. Bush concerning stem-cell research and gay marriage is wrong," he said on a recent show. "And that what he is doing with the FCC is pushing this religious agenda."
Levin dismissed what he called Stern's "conspiracy theories."
"The truth is Howard Stern was suspended because his conduct violates FCC regulations and puts broadcast licenses at risk," said Levin. "As popular as he is, that's a risk not worth taking."