Choo is scheduled to play for Round Rock On Wednesday. If all goes well, he could be activated on Friday against the Astros in Houston.
"I talked to him on the phone today and he was very upbeat with his progress," Rangers manager Jeff Banister said. "Let's get him through tomorrow and see where he's at."
Darvish, who had Tommy John elbow reconstruction surgery on March 17, 2015, completed his fourth start Tuesday pitching for Double A Frisco against Midland. He threw 68 pitches over five innings and pitching coach Doug Brocail was impressed while watching it on MiLB.TV.
"It was good," Brocail said. "He was on both sides of the plate with his fastball, he threw a lot of strikes and was down with a lot of pitches. That was something that's nice."
The Rangers haven't made a final decision on the next step but it could be pitching six innings and 90 pitches for Frisco on Sunday.
"I don't think it's necessary to rush anything," Banister said. "Keep him on the pace of what he has been doing."
Profar playing second: The Rangers had been using Jurickson Profar strictly at shortstop for Round Rock but he played his first game at second base on Tuesday. The Rangers want Profar to be ready for when Rougned Odor serves his suspension.
The Rangers can't replace Odor on the 25-man roster. But they will likely add an infielder for depth and go one pitcher short in the bullpen while Odor is out. Profar has come back strong this season after missing two years because of a torn muscle in his right shoulder.
Odor was suspended for eight games by Major League Baseball on Tuesday but his appealing the decision.
"We'll make a decision if we need to make a move at that point," Banister said. "But we think it's necessary for Profar to play second base."
• Right-hander Kyle Lohse, who was signed as a Minor League free agent by the Rangers last week, made his first start at Triple A Round Rock on Tuesday and allowed three runs in 5 1/3 innings. He allowed six hits, walked one and struck out four over 84 pitches.
• Rangers catchers went into Tuesday's game with a combined slugging percentage of .477, the highest in the American League.
T.R. Sullivan has covered the Rangers since 1989, and for MLB.com since 2006. Read his blog, Postcards from Elysian Fields, follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.