The 48-year-old driver from Dawsonville, Ga., who announced his plan Tuesday, is running a limited schedule this season.
He has seven top-10 finishes in 10 races at Indianapolis Motor Speedway, including a victory in 2002. Elliott has completed 1,599 of 1,600 total laps in the Brickyard's history.
The Brickyard would be his second NASCAR Nextel Cup start of the season. He raced in April at Texas Motor Speedway. Elliott also was in the non-points Bud Shootout at Daytona in February.
Elliott has won 44 races and was the 1988 Cup champion.