The game is likely to be played on Sept. 10, 2016, the source said.
The Bristol Motor Speedway Commission announced plans for a news conference Monday at the track for what it called a major announcement, but gave no details.
"I can just tell you I'm going to be in Bristol on Monday from about 11 to 1," Virginia Tech athletic director Jim Weaver said in a telephone interview Wednesday night. He said football coach Frank Beamer would be there as well.
"I think it has the chance to be a really nice event," Weaver said, adding that the idea has been in the works for "three or four months."
Tennessee athletics spokesman Jason Yellin said the school could not comment.
This is an event that had been talked about for years. It is unknown exactly where the playing field will be placed relative to the track and infield, which is composed entirely of asphalt.
The Bristol Motor Speedway location makes it ideal for fans from both teams to get to. It is about halfway between the two campuses on Interstate 81, 110 miles northeast of Knoxville, Tenn., and 125 miles southwest of Blacksburg, Va.
Information from The Associated Press was used in this report.