Rodriguez, out since July 8 with a torn meniscus in his right knee that was surgically repaired July 11, is scheduled to be the designated hitter in a minor league rehab game Friday in Florida and to play third base in a game Saturday.
After that, Rodriguez's fitness to return to the Yankees' lineup will be re-evaluated.
"Will we have him in Kansas City? I don't know," Girardi said before Thursday afternoon's game between the Yankees and Los Angeles Angels. "I would think by Minnesota we would have him."
After this weekend's series with the Tampa Bay Rays, the Yankees travel to Kansas City for three games with the Royals beginning Monday night, then travel to Minneapolis for four with the Twins beginning Aug. 18.
"We'll have to build him up," Girardi said. "I think the most important thing is that he feels comfortable and that he feels that he's moving freely."
At the time of his injury, Rodriguez was batting .295, but his power numbers were down -- 13 home runs, 52 RBIs and a .485 slugging percentage, fourth-best on the team behind Curtis Granderson (.579), Robinson Cano (.519) and Mark Teixeira (.517).
In his absence, the Yankees have not suffered a power outage.
Teixeira, who has taken over most of the cleanup-hitting duties, leads the team with 32 homers and is just one behind the major league leader, Jose Bautista of Toronto. And Granderson, moved down to the No. 3 slot normally occupied by Teixeira, leads the team in RBIs with 91, one behind major league leader Adrian Gonzalez of Boston.
Rodriguez still awaits a meeting with baseball officials about his alleged involvement in high-stakes poker games.
Major League Baseball started an investigation after Star magazine reported last month that several people saw him playing in games hosted at Hollywood hotels and residences.
"I'm looking forward to (the meeting)," Rodriguez said Wednesday. "I'm concentrating on baseball."
No date for the meeting has been announced.
Wallace Matthews covers the Yankees for ESPNNewYork.com. Information from the Associated Press was used in this report.