Lionsgate - the studio behind the massively successful film - is reportedly courting the Twilight star for the part of District 4 tribute Finnick, a handsome winner of one of the previous Hunger Games, according to Think McFly Think.
The studio has refused to confirm or deny the report.
"As with the first film, we won't be confirming, denying or commenting any casting rumours for this title," Lionsgate told the Huffington Post in a statement.
"We will announce news wide when there is official casting news to announce."
Catching Fire is currently set to begin filming in the autumn for a November 2013 release date.
Toy Story 3 scribe Michael Arndt is working on a re-write of the Catching Fire script from Slumdog Millionaire writer Simon Beaufoy.
I Am Legend's Francis Lawrence will helm the sequel following the departure of Hunger Games director Gary Ross.
Watch Robert Pattinson in the teaser trailer for upcoming film Cosmopolis below: