Mayhew says Friday that Goodell had indicated he would make a decision about Detroit's defensive tackle "well before" the season starts.
Jackson was on a list of players last season accused of using a diuretic, which can serve as a masking agent for steroids. He was not suspended.
The NFL Players Association has a federal appeal pending in an attempt to aid Kevin Williams and Pat Williams of the Minnesota Vikings and three other players suspended for the same alleged violation. The other players are New Orleans' Charles Grant and Will Smith and former Saint Deuce McAllister.