NASCAR is switching to a new Sprint Cup car next season and the additional tests would help teams adjust to the vehicle.
NASCAR has banned testing since 2008 at tracks that are host to NASCAR-sanctioned races in an effort to reduce costs for teams.
NASCAR officials have told team officials, however, that it is considering easing the ban next season.
"We told them there's a bunch of things we're looking at for next year … whether it's the testing policies and things like that," Robin Pemberton, NASCAR vice president of competition, told Fox Sports.
"Knowing that the teams, quite a few of them now as the economy has gotten better for them, venture out and test at more places more often, it's time to look at that again because it's obvious that the best and the most quality testing is done at the tracks that host our events."
At least one team owner, however, is against the idea.
"Right now, under the present economic circumstance with sponsors and teams, to open the testing policy is a bad economic move," Jack Roush told Fox Sports. "It would cost the teams more money to be able to test. The testing that makes the most sense is the testing at Michigan and Pocono where you test the day before the race.
"But to have open testing, to go wherever you want whenever you want, is unnecessary and costly."
Source Sporting News.com