Details of the agreement were not immediately released. Irsay was arrested in March on two misdemeanor charges and was scheduled for an Oct. 30 trial.
But the Star, citing online court records, reported that a change of plea hearing has been scheduled for Tuesday.
"I cannot provide any details of -- or even verify the existence of -- an agreement unless and until one would be tendered to the Court at such a hearing," Andre Miksha, a spokesman for the Hamilton County prosecutor, said.
Once a plea agreement is reached, it would allow NFL commissioner Roger Goodell to begin rendering punishment for Irsay.
Irsay was arrested March 16 near his home in the Indianapolis suburb of Carmel after he was spotted driving slowly, stopping in the roadway and failing to use a turn signal. Officers said he had trouble reciting the alphabet and failed other field sobriety tests.
A police report said various prescription drugs were found in his vehicle, along with more than $29,000 in cash.