"He's still experiencing soreness," Cashman said in a telephone interview. "All I can tell you is, he has still experienced soreness and our doctors are working through it."
The club estimated that there was a 30-percent chance Teixeira would need surgery after he partially tore the tendon sheath in his wrist in March, a number that remains in play.
"You want someone that's feeling great," Cashman said. "They've never taken surgery off the table. It's always been obviously the worst-case scenario, but I'm not here to tell you anything about that yet."
After missing the first two months of the season, Teixeira made his return on May 31, only to leave New York's June 15 game against the Angels early when he felt unable to swing the bat.
"You guys know me, I'm going to play through everything, but if I literally can't [swing], I was worthless to the team right there," Teixeira said last week. "So I said, we need to get this looked at."
In his brief return, Teixeira hit .151 with three home runs and 12 RBIs in 15 games. He went hitless over his last four games and said that the soreness affects him most when batting left-handed.
Though Teixeira said there is little discomfort when he hits right-handed, both he and manager Joe Girardi shot down a suggestion that he could finish the season as a platoon player against left-handed pitching.
"It's not something that we've discussed, so I can't answer the question," Cashman said on Monday.
With Teixeira back on the disabled list, Lyle Overbay has returned to everyday duty as New York's first baseman. Cashman said that he could not speak to how Teixeira's injury situation might affect his mindset toward acquiring another first baseman over the next month.
"Right now, until I have an official position [about surgery] and not the fact that he's still experiencing soreness, there's really not much more to say," Cashman said.