"Then we'll have some results and decisions to make," Acta said.
Hafner's back flared up during a July 31 game against Kansas City, and it has caused him to miss four games thus far. Acta originally expected Hafner to be ready to play on Tuesday, but the injury hasn't gotten better.
Hafner, who has played in only 60 games this season, missed more than a month after having knee surgery earlier in the year. He's hitting .239 with 11 home runs and 32 RBIs this season and will be a free agent at the end of the year.