The switch-hitting Teixeira is batting .244 with 37 home runs and 106 RBIs, but from his non-natural left side, he has hit just .221 (87-for-393) and has frequently hit into defensive shifts.
Manager Joe Girardi said that a change is something the Yankees have been talking about. He said the real motivation was the red-hot Cano, who entered play Tuesday hitting .305 with 28 homers and 118 RBIs.
"You kind of go by how guys are going, obviously," Girardi said. "Robbie, we saw what he did last year in the last two months and in the postseason. That's kind of Robbie's M.O.; it seems like he gets stronger as the year goes on."
Cano said that he recognizes increased responsibilities in hitting third, ahead of Alex Rodriguez and Teixeira.
"You have to do everything right," Cano said. "You're going to get pitches to hit, because you've got a guy behind you that they don't want to face, either.
"It's a situation now where I'm going to get better pitches, so I have to continue doing what I'm doing right now. That's not going to change my mindset; I'm going to keep playing my game and swing at strikes."
Teixeira had not batted fifth to start a Major League game since 2004, when he made 67 starts in that slot for the Rangers.
"Really, at the end of the day, it really doesn't matter at all," Teixeira said. "I've hit third, fourth, fifth, and I hit fourth behind Chipper [Jones], which was great.
"I've hit third the majority of the time here. Like I said, Robbie's really hot right now. As we go into the playoffs against right-handed pitching, why not have him there?"