"That's the hope," general manager Brian Cashman said in a phone conversation Wednesday. "We'll see through the weekend. We started the 20-day rehab and once we felt he could complete the 20 days and be available to us in Texas. So let's get through the weekend and see where he is at and see if he is major league able."
Cashman said the Yankees could activate Rodriguez on Monday in Texas or give him an additional day off and push his first game to Tuesday.
"We have to get through the weekend, and then we will evaluate it," Cashman said.
If the Yankees were to decide that Rodriguez wasn't ready to return, he would remain on the disabled list. He would then work out for a period of time before going on another rehab assignment.
Rodriguez, who will turn 38 in less than two weeks, is trying to return from a second hip surgery. He has not played in a major league game since the 2012 postseason in which he went 3-for-25 with 12 strikeouts. He was pinch-hit for and benched during the playoffs.
Ten games into his rehab stint, Rodriguez is 5-for-28 with one home run and six strikeouts. Beginning Thursday, Rodriguez will move to Triple-A Scranton/Wilkes-Barre.
"We're on schedule," Rodriguez said Wednesday morning.
Rodriguez just worked out Wednesday morning but said he felt fit enough to appear in a game.
"After playing four straight games, seven or eight plus innings, and being able to play today if I had to, that's a great sign," he said.
Rodriguez said he has checked off every box on his rehab, except breaking up a double play.
Looming above all of Rodriguez's future plans is the Biogenesis scandal. Rodriguez is expected to be suspended when the penalties come down. There is no set date when they will be announced, though they are expected at some point in the second half of the season.
However, players' association executive director Michael Weiner said the appeal process may take long enough that suspensions would not take place until 2014.
If that were the case, it may help the Yankees with their goal of getting under $189 million to take advantage of financial incentives in the collective bargaining agreement.
For every 50 games that Rodriguez would be suspended, the Yankees would save around $7.5 million.
ESPNNewYork.com's Ian Begley contributed to this report.