Britt faces misdemeanor charges filed by the Tennessee Highway Patrol of twice making inaccurate statements on his application for a driver's license.
The (Nashville) Tennessean said Tuesday it was believed Britt wasn't truthful when he was asked whether his license had been suspended in the past.
"We would anticipate that he would report and surrender himself on these and let them be served when he returns to the state of Tennessee," Nashville Metro police spokesman Don Aaron said. "If he does not, he'll be subject to arrest."
Britt's lawyer told the newspaper he would cooperate in the matter. Britt was arrested last week in New Jersey on charges related to allegedly smoking marijuana behind the wheel.
The Tennessean said Britt has had at least nine brushes with the law since he was drafted by the Titans in 2009.