Obada is a free agent after recently terminating his contract with Free State Stars just four months after his arrival in Bethlehem.
According to a source in the Dube Birds camp, Obada and ex-University of Pretoria midfielder Philani Khwela are on trial in Soweto.
"We first saw them at our training grounds just before the Christmas break. But since we've re-opened they've been training with us all the time.
"If they impress the coach, they will join us."
Swallows, who were relegated from the Absa Premiership at the end of last season, are 14th on the NFD standings with 10 points from 13 games.