The reports started after Lawrence and the Australian actor were spotted joking around on the red carpet at the movie's London premiere.
The Daily Telegraph then reported that "rumours [about the pair] are swirling throughout Hollywood."
The publication also reports, "the co-stars are often seen having private moments, chatting and giggling together".
Previously Lawrence was in a relationship with filmmaker Darren Aronofsky (who she worked with on mother!), while Edgerton was once engaged to Balinese fashion designer Alexis Blake.