David Lane, one of Churchill's lawyers, said a settlement could be reached "quickly," but the parties have to agree on the final language.
"I don't think there are any sticking points. It's just a matter of drafting an agreement that's acceptable to everyone," he told the newspaper.
Churchill has been the embroiled in controversy over an essay in which he compared some of the victims of the Sept. 11, 2001, terrorist attacks to a Nazi Adolph Eichmann.
In February, the CU regents ordered a review of Churchill's writings and speeches to determine whether there is cause for the tenured professor to be dismissed.
The review panel received documents this week purporting to show Churchill plagiarized the work of a professor at Dalhousie University in Nova Scotia, the News reported. Churchill could not be reached for comment on the report.
A CU spokeswoman said this week that the findings of the investigation would not be known until at least Monday.
2014: The Year in Music [PHOTOS]