Darvish, on the DL because of discomfort and tightness in his right shoulder, is scheduled to make his second start on a rehabilitation assignment Sunday for Double-A Frisco.
Darvish is scheduled to throw 60 pitches. If all goes well, the Rangers will deliberate whether to activate him to pitch on Saturday against the Cubs or if he needs a third start in the Minor Leagues.
"We'll see how Sunday goes," Banister said.
Banister said he is leaning toward using Cole Hamels next Sunday in the third game of the series against the Cubs. Banister wanted to give Hamels a little extra rest going into the second half.
Hamels will be at the 2016 All-Star Game presented by MasterCard on Tuesday in San Diego and the Rangers are hoping he'll be limited to one inning. Hamels will be making his fourth trip to the All-Star Game and his first in his hometown of San Diego. He was limited to one inning in two previous All-Star appearances and did not pitch in the other.
"We try to ask (National League manager Terry Collins) to limit the number of innings," Banister said. "While the game is important, I think they are responsible enough to use him the right way. It's a great honor for him to make the All-Star team, go home and pitch in front of the home crowd."
Banister on NL vs. AL
Banister spent 29 years in the Pirates organization learning to play by National League rules before becoming an American League manager with the designated hitter.
So what is his preference?
"I prefer both," Banister said. "I think our game needs two leagues that are different. If not, why don't we put all teams in one league? That won't be any fun. They are distinctively different.
"There are advantages when the American League team goes to the National League park. The advantage goes to the National League team. There is still an advantage to the American League team when the National League team comes to their park. I love the fact we have distinctive leagues."
• First baseman Mitch Moreland was in the starting lineup for the first time in seven games. Moreland has been dealing with a tight right calf muscle and said, "I still feel it a little bit but it is much better."
• Kyle Lohse, Saturday's starter, is the 10th starter used by the Rangers this season. Only Oakland has used more (11). The Angels have used 10.
• Banister said there were no innings limits on Lohse in his first start. Said Banister, "Based on the last seven games, I hope it's five."
• Reliever Keone Kela, who is on the disabled list recovering from right elbow surgery, threw a scoreless inning for Double-A Frisco in a rehab assignment. It was his third scoreless appearance. Kela is scheduled to pitch again on Sunday night and if all goes well, he is expected to be activated on Friday in Chicago.