The New York Times has reportedly obtained the draft of a complaint with a threat from Baffert.
He said he will sue the track unless it lifts the two-year suspension received after Kentucky Derby winner Medina Spirit failed two post-race drug tests.
With the ban in place, horses trained by Baffert cannot race in the Derby or Oaks.
“CDI is committed to protecting the integrity and future of the racing industry – for the horses, our fans, our partners, our team members and the betting public,” a statement from Churchill Downs Incorporated read. “No one is above the rules, including Mr. Baffert, and we remain intent on holding him accountable for his actions.”