Smith was released earlier this season by Miami, and worked out for the Browns on Tuesday, said the person who spoke to The Associated Press on condition of anonymity because the contract has not been finalized.
The Browns need a kick returner after Pro Bowler Josh Cribbs dislocated toes in Sunday's loss to the New York Jets. Cribbs could be out for some time, leaving rookie Joe Haden as Cleveland's primary returner.
NFL.com earlier reported the possibility of Smith's signing.
Smith made Tampa Bay's roster as an undrafted free agent in 2008. He made the Pro Bowl as a rookie after becoming the first player in club history to return a kickoff and punt for touchdowns in the same season. He finished last season on injured reserve with a concussion.