Andriese (right hip stress reaction) threw three innings in a simulated game on Tuesday. Rays manager Kevin Cash then told reporters on Wednesday that Andriese "felt really good" a day after his stint.
"He'll throw a bullpen [session] tomorrow," Cash said.
Andriese, who is 5-1 with a 3.54 ERA in 12 starts this season, still needs to be stretched back out before he can finish his rehab. He is expected to be inserted back into the rotation once he returns.
Kiermaier (right hip fracture) had been on a rehab assignment when he experienced a setback in the form of a stiff back. After several days off to let the back pain subside, the American League Gold Glove Award outfielder appears to be close to heading back on a rehab assignment.
"I think if all goes well today [with Kiermaier], which to my knowledge it has, he'll most likely hit on the field tomorrow," Cash said.
Kiermaier is hitting .258, with seven home runs and 20 RBIs in 62 games this season.
Both Kiermaier and Andriese are expected to be back with the team by mid-to-late August.
Bill Chastain has covered the Rays for MLB.com since 2005. This story was not subject to the approval of Major League Baseball or its clubs.