"It's going to be pretty tough [for them to play]," Girardi said.
Girardi added that he will check daily with Teixeira, who has required three cortisone injections this season in his surgically repaired right wrist. Teixeira said that he would prefer to play, even with the Yankees mathematically eliminated.
"I plan on it," Teixeira said. "I haven't talked to Joe or the medical staff. It's their final decision, but I plan on it."
Beltran, 37, was envisioned as the Yankees' everyday right fielder after signing a three-year, $45 million contract last offseason, but he was able to play just 32 games in the outfield because of injuries, appearing in 76 games as the designated hitter.
Beltran batted .233 with 15 home runs and 49 RBIs in 109 games, and his recovery time is expected to be 12 weeks, so he should be ready for Spring Training.
Ellsbury, 31, produced better results in the first season of a seven-year, $153 million contract and said this week that he was hoping to return to the field before season's end.
The center fielder batted .271 with 16 home runs and 70 RBIs in 149 games, his most games played since 2011.
Teixeira went 2-for-4 with a double, a homer and three RBIs in Wednesday's loss and is batting .219 with 22 homers and 61 RBIs in 121 games. He sums up his year as "not good."
"Obviously, the first half I battled through some things, and I felt good about my first half, but the second half has been terrible," Teixeira said. "I've been saying it for the past few weeks: I need to get stronger, I need to get healthier and hopefully not have those issues that I've had the second half of the season."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.