The Astros travel to Kauffman Stadium for two games against the Royals on July 20-21.
McCullers will start the first game, which is scheduled for 7:05 p.m. CT. James will start the second game, which is scheduled for 1:05 p.m. CT.
Strom said not to worry about James' readiness.
"I think you're going be very pleasantly surprised with Josh James," Strom said. "Josh James started this whole program months ago down in Florida. He and I stayed in contact. We utilized Gerrit Cole as kind of a model. A lot of time in teaching, modeling is the way to go. And Cole would be one of the best. So we've cut down on a lot of the extraneous movement that James had been seeing before. A lot of misses took place and he's kind of tighten things up a little bit. I've monitored every one of his bullpens that he's thrown when he was down in Florida.
"It's not going to be a slow walk with Josh James. He's built up to four innings already, I believe. I think that's what we'll see the first time out. If he has a good four, we may extend him to five. So we're in great shape in that position right there."
McCullers increased his pitch count in Tuesday's intrasquad game. He threw 74 pitches in five scoreless innings Tuesday, up from his 67 pitches in four innings in last Thursday's intrasquad game.
McCullers' velocity was down Tuesday, and Strom attributed that to missing Sunday's workout after the pitching staff was held from the ballpark due to a potential exposure to the coronavirus.