Teixeira said he didn't feel 100 percent, but after running 10 to 12 sprints close to full speed, he had some optimism that he might be able to return as early as Friday.
"We're always going to try to come back as quickly as we can, so we'll have that conversation," Teixeira said. "I would have loved to have been back today, but it wouldn't have been ready today."
Teixeira has not played in the last eight games, and manager Joe Girardi said that they must be cautious not to rush Teixeira back for fear of losing him the rest of the way.
"I think it's a matter of making what's the best decision for him and us, moving forward," Girardi said. "If a guy's not ready, you put him out there and get him injured again, he's done for the year probably. That's the balancing act we have to do."
Teixeira said that the tight American League East race is pushing him to get back sooner than he might have if the Yankees still had a large cushion.
"Obviously if we're up 10 games, I'm probably going to take that extra day or two," Teixeira said. "When we're fighting right now for the lead, I'm going to try to come back as quickly as possible. This is the way it is. I want to be out there really badly right now."