Unser, a two-time Indy 500 winner, was arrested in January for driving under the influence of alcohol near his home in Nevada.
He said he doesn't think the DUI arrest should keep him off the racetrack, the Indianapolis Star reported Wednesday.
It would be Unser's 19th start in the race.
Unser will be inducted next month into the Indianapolis Motor Speedway Hall of Fame, joining his father Al Unser Sr. and his uncle, Bobby Unser.
Celebrity Families of 2014 [PHOTOS]