The exception can be used by a team over the salary cap to replace a player who is out for the season and must be applied for before Jan. 15.
If granted, the team can use the exception because of the season-ending knee injury suffered by forward Josh McRoberts. Miami can offer $2.65 million to Smith, who was released Monday after less than two seasons with the Detroit Pistons and more than $26 million left on his contract.
Once Smith clears waivers, he is free to sign with any team.
The Houston Rockets, Dallas Mavericks, Sacramento Kings, Los Angeles Clippers and Memphis Grizzlies are also reportedly interested in Smith, who averaged 13.1 points, 7.2 rebounds and 4.7 assists in 28 games this season for Detroit.
"I think we can use an athletic big," Mavericks guard Rajon Rondo said. "They traded me for Brandan Wright. Besides Tyson [Chandler], our other bigs are perimeter shooters. Josh brings a lot to the game -- his intangibles, he can make plays, rebound, defend. He'd be a good fit anywhere, but especially here I think he'd be a good fit."
Smith, 29, is shooting 39 percent from the field and 47 percent from the free-throw line. Only two other players in the NBA shoot a worse percentage from the line than Smith.
- Scooby Axson