Miller is most familiar for is Oscar-nominated sports movie Moneyball, while Lawrence is known for his work on Water for Elephants and I Am Legend.
Sources tell Deadline that executives at Lionsgate have narrowed down the choice for the Catching Fire director to these two names, after talks with other top contenders.
Among the "seven or eight names" targeted by Lionsgate were directors Alfonso Cuaron, Attack the Block director Joe Cornish, The Orphanage director Juan Antonia Bayona and David Cronenberg.
The search for a new director comes after Hunger Games director Gary Ross stepped down from the franchise, citing a busy work schedule for his inability to direct the next movie in the series.
Ross's film - starring Jennifer Lawrence, Josh Hutcherson and Liam Hemsworth as teens in a dystopian future - has earned over $400 million (£249 million) to date, staying at number one in the US box office for four weeks straight thus far.
An announcement as to who will direct will reportedly be made before the end of this week.
Watch a clip from The Hunger Games below: