Ramirez, on the disabled list since April 16 with right shoulder inflammation, made his second relief appearance with Double-A Tennessee on Sunday, striking out the side. He is expected to join Iowa on Tuesday in Des Moines.
Meanwhile, outfielder Jorge Soler did some agility work in the outfield Sunday and was to hit in the batting cages. There is no timetable set for when Soler, out since June 3 with a left ankle sprain, will begin a rehab assignment.
Soler was batting .265 with four home runs and 12 doubles in 49 games before he was injured.
• The Cubs have a tough seven-game stretch coming up against two division leaders, the Dodgers and Cardinals. Manager Joe Maddon welcomes the challenge.
"It's a good thing to be playing really good teams," Maddon said Sunday. "It's good for our guys. The only way we'll get better is to play teams that are good, like the Twins right now.
"You have to repeat fundamentals over and over against those guys. The team that doesn't blink wins. It clearly comes down to that."
• Entering Sunday, the Cubs played 10 extra-inning games this season, the most in the Majors. They're 7-3 in those games, and they're batting .365 (27-for-74) with 14 runs scored in extra innings, which are both tops in the Majors.