The actress, 23, played the role of District 1 tribute Glimmer in the Jennifer Lawrence starer franchise, reported Us magazine.
"Leven and Jason are hooking up and dating," according to a source.
The former soap star has posted several photos on Instagram cuddling with Trawick.
"She really likes him," the source added.
Trawick began dating Spears in 2009, and the couple got engaged in 2011, only to split in January 2013 after several reports of trouble in paradise.
Spears, 31, too has moved on and is currently dating David Lucado.