The All-Star third baseman has not played since leaving Sunday's game in Baltimore because of a strained right quadriceps. He got treatment in New York on Monday, then went to Miami to join his wife, who gave birth to the couple's second daughter. He passed out cigars Thursday in the clubhouse to celebrate.
He said his leg has improved but he still needs to test his mobility before he can play.
"Leg's good. I got treatment the last several days at the University of Miami," Rodriguez said. "I've not run on it yet, just hit. Felt pretty good."
Rodriguez said he hoped to return to the lineup Friday night for the start of a three-game series in Cleveland against the Indians, the team that beat the Yankees in the AL playoffs last fall.
Rodriguez said manager Joe Girardi will make the decision, depending on how well he can move.
"Since the injury I have not run," Rodriguez said. "He's going to make up his mind after he sees me move around a little bit and go through my routine. He's contemplating maybe DH one of the days over the weekend and then go down to third base."
With rain falling before Thursday's game at U.S. Cellular Field, the Yankees will have to wait to gauge Rodriguez's readiness Friday at Progressive Field.
"We'll make an evaluation tomorrow and we hope to get him in there during the Cleveland series at some point," Girardi said.
"You can't predict when you work a guy out how his leg is going to react. The big thing is we have to make sure he doesn't re-injure it," Girardi added. "If you re-injure it, it's probably going to be worse. And we can't really do much with him today because of the conditions. So we'll have to see tomorrow."
Rodriguez said the injury doesn't bother him walking around.
"But I felt it kind of playing with my daughter two days ago, trying to get up from the floor. I got to see. The big test is going to be running."
Rodriguez said he didn't expect to go on the disabled list.
"I have a a pretty good feel. I'm optimistic that it's going to be nothing past this weekend," he said.
Morgan Ensberg has started in place of Rodriguez, who is batting .308 with four homers and 10 RBIs.
Ensberg, who is also batting .308 with one homer and one RBI, was back in the lineup Thursday.