The 33-year-old Rodgers managed only 15 appearances in all competitions for the Clever Boys, scoring two goals, while Mthembu played 30 games and netted six times.
Mthembu’s contract with Ea Lla Koto will expire at the end of this month.
"I think we will finalise with a local striker," Eymael tells KickOff.com.
"We wanted Rodgers but Rodgers is hesitating. Another one we are targeting is a South African, so it's two South Africans and one foreigner. Mthembu has not yet renewed so we will sign another local one.”
Rodgers has struggled to get regular game-time in the starting line-up, as coach Gavin Hunt prefers using Lehlohonolo Majoro. His chances of playing next season are slim, so a move could do him well.