However, Rodriguez is unlikely to be ready to rejoin the Yankees on Monday in Kansas City, manager Joe Girardi said Wednesday.
"My guess would be no, but I can't tell you for sure," Girardi said. "It depends how he feels each day. But would I say at the beginning of the Kansas City series? No."
Girardi said that it's possible Rodriguez will be the designated hitter on Friday and play the field on Saturday for either the Gulf Coast League Yankees or the Class A Tampa Yankees.
"Then we'll see where he's at," Girardi said.
Girardi said it's realistic that Rodriguez will be back at some point during the team's road trip next week.
"Yes, that's our hope," Girardi said.
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.
Rodriguez has been out since July 7 with a torn meniscus in his right knee. He elected to have surgery to repair the tear on July 11 in Miami after seeking a second opinion.
Rodriguez was expected to miss four to six weeks at the time of the injury. If he returns next week, he will have missed about five weeks.
The Yankees have gone 18-11 in his absence. The 36-year-old was hitting .295 with 13 home runs and 52 RBIs in 80 games before going down.
Rodriguez has been rehabbing at the team's spring training facility in Tampa, Fla..
He ran the bases and took ground balls on Tuesday, and has been taking batting practice the past few days.
"It's all good stuff," Rodriguez said.
Girardi did not have a report on how his Wednesday session went.
Mike Mazzeo is a regular contributor to ESPNNewYork.com. Information from the Associated Press was used in this report.