That swap of standout first basemen would go down as one for the ages, but Teixeira -- who has a no-trade clause on his eight-year, $180 million contract -- says it's not going to happen.
"I'm not going anywhere," Teixeira said. "I've got that no-trade for a reason. I'm going to be buried in these pinstripes."
As he enters the third year of a deal that runs through 2016, the 30-year-old Teixeira reported to camp on Saturday and will go through his first workout Sunday with the Yankees' other position players.
He said that he has healed completely from the injuries that dented his 2010 season, including the right hamstring injury that knocked him off the Yankees' playoff roster in the American League Championship Series.
"It's over," Teixeira said. "I play hard, I'm going to get hit with pitches, I'm going to dive and jam stuff. You've just got to play through it and hope for the best."
Reflecting on a season in which he batted .256 with 33 home runs and 108 RBIs in 158 games, Teixeira said that the most difficult obstacle he faced was the deep bone bruise on his right hand, which he suffered while diving in an Aug. 28 game at Chicago's U.S. Cellular Field.
He also broke his right pinky toe when he was hit by a pitch from the A's Vin Mazzaro on Aug. 31.
"At times I felt bad for Mark, how beat up he was last year, going out there and playing," Yankees manager Joe Girardi said. "It's tough when you have to go through so much just to get out on the field. You don't necessarily feel like you can move. Every time he dove, I cringed."
Teixeira has been a notoriously slow starter, batting just .136 in April last season, and he is hoping to shake that stigma by hitting more now.
He said that he worked out at Bobby Valentine's sports academy in Connecticut over the winter, even purchasing a new pitching machine for the facility, and said he is focusing on making his left-handed swing more consistent.
"It's still unnatural," said Teixeira, who posted a .799 OPS left-handed and a .940 OPS right-handed. "At the end of the day, no matter how long I've been playing baseball, I'm still a right-handed hitter who also switch-hits. I just have to work harder at it.
"My attitude this year is if I have a half hour, instead of putting it in the gym lifting weights, let's put it in the cage and make sure that left-handed swing is consistent."
He also asked hitting coach Kevin Long to be more critical in the batting cages, wanting to ward off the demons of the season's first month.
"April hasn't been fun the last couple of years for me," Teixeira said. "It's not something that I enjoy. I don't enjoy failing. I want to go out there and get a hit every time up.
"I told K-Long, 'Give me some tough love if I need to. Don't tell me I'm doing OK if I'm not.' I want to make sure that on March 30 that we're ready to go."
So Teixeira also wants the fans to put any Pujols fantasies on hold -- a deal the Yankees haven't been interested in discussing anyway, according to a source with knowledge of the club's thinking. The only place Teixeira plans on being is Yankee Stadium.
"I'd be disappointed if the fans of New York weren't looking to make our team better," Teixeira said. "But they've just got to know that I'm not leaving."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.