Per Heavy.com's Sean Deveney, Augustin is among "a number of potential veteran backup point guards" the Lakers have inquired about leading up to the Feb. 6 trade deadline.
The Lakers' reported interest in Augustin comes in the wake of Darren Collison being linked to the team.
Per ESPN's Adrian Wojnarowski, Collison is considering ending his retirement to return to the NBA in February, with the Lakers and Los Angeles Clippers his preferred landing spots.
Augustin has taken on a backup role with the Orlando Magic this season thanks to the emergence of Markelle Fultz. The 32-year-old is also having issues finding a shooting rhythm. His three-point percentage has dipped from 42.0 percent the previous two seasons to 33.9 percent in 35 games this season.
The Magic are eighth in the Eastern Conference standings, but their 16-19 record is disappointing coming off last year's 42-win campaign. Augustin is a logical trade candidate for the team given his age and being in the final season of his contract.
The Lakers can use additional shooters as they look to solidify their roster for a potential playoff run. Augustin hasn't shot up to his potential thus far, but he's got a 38.0 percent success rate in his career from three-point range.