Judge Larry Naves said he expects to make a decision by next week, The Denver Post reported Thursday. Naves heard testimony and arguments Wednesday.
The judge's options include ordering Churchill's rehiring, a financial payment or nothing.
A jury decided this year the university fired Churchill because of a notorious essay he wrote calling some of the victims of the 2001 terrorist attacks "little Eichmanns." Jurors awarded him only $1 in damages.
The university maintains Churchill was dismissed because he plagiarized some of his work and did shoddy research. Todd Gleeson, dean of the College of Arts and Sciences, said having Churchill on the faculty in ethnic studies "taints the department."
Churchill and his supporters say the issue is academic freedom.
"Political interests -- whether internal or external to the university -- do not have the prerogative to remove professors or to silence them because of disagreements for their beliefs," Churchill testified.