Williams was arrested on a DUI charge in the early morning on April 3. Williams has pleaded not guilty to the charge.
His attorney, Jonathan Simon, told NFL Media Insider Ian Rapoport that it would be "unusual" if Williams' DUI case is resolved in 20 days, meaning before the start of the draft.
"If they are going to litigate, we are going to defend it," Simon said.
Simon also said, "There is a disputed version of events," not revealing details.
In an ideal world, Simon said Williams' legal issues -- which could cause him to slide on some draft boards -- would be resolved before the draft, but that is unlikely to happen.
"We don't want P.J. treated differently from anyone else because he's a good player," Simon said. "This is not a situation where we're looking for him to be pushed through the system. ... This is not what you want to have happen, but we don't want any special treatment."
Williams is the No. 35 player on NFL Media analyst Daniel Jeremiah's list of the draft's top 50 prospects.