Mark Teixeira still has soreness in his right wrist following a June 16 cortisone shot and a week of rest, an ominous sign for the ailing Yankees first baseman.

“Certainly, our hope had been that by this point, he would be OK,” general manager Brian Cashman said yesterday. “Obviously, that’s not the case, which isn’t good. It’s not what we wanted.”

Season-ending surgery has been a possibility since Teixeira suffered the partially torn tendon sheath during spring training while preparing for the World Baseball Classic. Initially, Cashman thought the chances of surgery were 25-30 percent.

The longer the injury lingers, the greater the chance the first baseman will have to go under the knife, as the Blue Jays’ Jose Bautista did a year ago when he had a full tear of the sheath.

“It’s clearly not a good situation,’’ Cashman told NJ.com.

But Cashman said the decision on surgery has not been made. Teixeira underwent an MRI exam last Sunday that showed only inflammation, which gave the Yankees hope he still would be able to avoid surgery.

“Our doctors are still trying to work through it,” Cashman said.

The switch-hitting Teixeira felt soreness swinging from the left side. He had just three hits in 40 plate appearances as a lefty since returning — though two of those were home runs.

In Teixeira’s absence, the Yankees have relied on Lyle Overbay at first. The Yankees held on to Overbay when Teixeira returned from the disabled list on May 31 as insurance for this very sort of setback.

But with injuries up and down the roster, there is only so long the Yankees can compete with such a weak lineup.

When asked whether the absence of Teixeira — and Derek Jeter and Alex Rodriguez and Curtis Granderson and Kevin Youkilis (whew) — has taken a toll on him and the team, Robinson Cano said, “Of course.”