BOSTON — There is a very good chance the Yankees will try to catch the Blue Jays or secure a wild-card spot without Mark Teixeira.

The switch-hitting first baseman and cleanup hitter underwent a second round of tests Tuesday in New York that indicated the bone bruise Teixeira suffered Aug. 17 when he fouled a ball off the lower right leg hasn’t made a bit of progress.

“His bone bruise hasn’t healed at all,’’ general manager Brian Cashman said before the Yankees’ 3-1 win over the Red Sox on Tuesday night at Fenway Park. “There is no stress fracture and that was our biggest worry, but the bone bruise hasn’t healed. He has some soft-tissue inflammation and inflammation around the nerve so he received some sort of an injection to calm that down. Obviously, the bone bruise is the big issue and there has been no healing. They put him back on crutches and we are looking at weeks.’’

Asked about the possibility Teixeira’s season is finished, Cashman looked where Teixeira is at and the baseball calendar.

“September is a month, and weeks means two. If it goes into three, you only have a week to get ready,’’ Cashman said. “He is going to be down for an extended period of time. It hasn’t been healing in any way, shape or form. Any other complications and it’s a timing mechanism. It’s a lot longer than anyone would have expected. It’s nothing he can do about and nothing we can do about it.’’

Since fouling the ball off his shin Aug. 17, Teixeira started one game Aug. 25, pinch hit the next night and hasn’t played since.

“The stress fracture has been ruled out, but you would have expected to see some sort of improvement on the bone bruise healing process and that hasn’t happened,’’ Cashman said.

Teixeira leads the Yankees with 31 homers and is second to Brian McCann with 79 RBIs.

Rookie Greg Bird has filled in for Teixeira and entered Tuesday night’s game hitting .250 (14-for-56) with two homers and 10 RBIs in 16 games. Because Bird is a lefty, manager Joe Girardi broached the idea he could start Alex Rodriguez at first against Red Sox lefty Henry Owens on Wednesday. Bird is 3-for-9 (.333) against lefties.

Tuesday’s news further emboldened the manager to think about that, even though Rodriguez, who has started one game at first this year (April 11), said Monday he wasn’t comfortable doing that. Nor did Cashman endorse the idea Monday and Tuesday.

“I think you have to really talk about it now,” Girardi said. “Because I think our hope was that, when we left on that road trip [last week], you would have Tex back by the time we got home [Friday], or even on the road trip. But now, I think you have to think about it because you’re going to see left-handers. There’s left-handers in our division. There’s a lot of division opponents in the last 32 games or whatever we have left. I think you have to start debating the idea.”

“I don’t think he can play first base,” Cashman countered.

On Monday, Cashman said that shifting Chase Headley from third base across the diamond was more likely.

“It’s something that we’ll talk about,” Girardi said. “I could put [Brendan] Ryan over there as an option. But it’s something we’ll talk about.”

Two Tuesday call-ups, Dustin Ackley and Austin Romine, also could be in the first-base mix, Girardi said, and Cashman seconded that notion on Tuesday.

— Additional reporting by Ken Davidoff