"We're aiming for Tuesday at home," Rodriguez said after working out at the team's minor league complex. "You've got to be smart, so it's a good way to go."
The All-Star third baseman is on the 15-day disabled list with a strained right quadriceps. He hasn't played since April 28 and is eligible to come off the DL this Thursday.
"Everyday it's much better," he said Tuesday.
Rodriguez, hitting .286 with four home runs and 11 RBIs, will miss the series this weekend against the crosstown rival New York Mets. He might be ready to play in extended spring training games this weekend.
Rodriguez took batting practice, fielded grounders and ran in the outfield during his latest workout.
"I ran about 90 percent today," Rodriguez said. "It felt pretty good running. I went from an 80 yesterday to about 90 today."
Rodriguez hasn't started running the bases, which normally is one of the final steps in a rehab program. He will remain in Florida when the Yankees finish a four-game series at Tampa Bay on Thursday, and expects to play third base immediately when he comes off the DL.
"I've got plenty of time down here to do all my work," Rodriguez said. "With our team, it's important for me to be at third base. It's frustrating because I feel like I need to be out there to help the team, but you've got to listen to the medical staff."
Rodriguez underwent a second MRI exam Monday, which showed improvement but also indicated the injury was not completely healed.
"Historically, I've been a good healer," he said.
Rodriguez met with team doctor Allen Miller after his workout, and then was in the Yankees' clubhouse three hours before Tuesday night's 2-1 loss in 11 innings at Tampa Bay.
"He's very happy with the progress of the MRI from last week to this week, so that's encouraging," Rodriguez said. "I think it's more precautionary now than anything else."
Jorge Posada threw for the second straight day, and also took batting practice. Yankees manager Joe Girardi said the catcher, sidelined by a right shoulder injury, could return early next month.
"Alex had another good day, and pushed it a little harder in the running and said he felt good," Girardi said. "Jorge said his arm felt a lot better today. So it's two good days."
Girardi caught RHP Andrew Brackman, who is coming back from right elbow ligament replacement surgery, during a 30-pitch bullpen session. The Yankees' first round pick in the 2007 amateur draft could be ready to pitch in instructional league this fall. ... RHP Humberto Sanchez (right elbow surgery) threw 35 pitches in a bullpen session. He could start pitching in minor league games around June 10. ... 3B Wilson Betemit (right hamstring) is taking batting practice, but has not resumed running. ... RHP Jeff Karstens (groin) was scheduled to pitch in his second extended spring training game Wednesday.
Information from The Associated Press contributed to this report.