"We're gonna bring him to Cincinnati, assess him," Hinch said. "There's a chance he is activated as soon as tomorrow, which would be great for our team, both morale-wise and production-wise."
Altuve has missed more than a month of action since being removed from a game on May 10. The six-time All-Star and 2017 American League MVP was initially diagnosed with hamstring discomfort before the injury was upgraded to a strain.
Altuve was later pulled from his minor-league rehab assignment near the end of May due to fatigue and soreness around his surgically repaired right knee.
He resumed his rehab earlier this week. Overall, he played five games at Triple-A Round Rock, hitting .190/.261/.286.
Before landing on the injured list, Altuve was slashing .243/.329/.472 with nine home runs and 21 RBIs for the Astros.