The American League presents stiff competition for the honor -- including the Tigers' Miguel Cabrera, the Rangers' Josh Hamilton and the Angels' Mike Trout -- but Jeter's performance at age 38 likely will earn him some space on a few ballots.
"Everyone would like to win an award like that," Jeter said. "You ask any player in baseball -- they would like to win an award like that. But I don't think you can allow yourself to think that."
Jeter, who entered Wednesday batting .324 with 12 home runs and 42 RBIs, said he is happy with some things that have happened this year but that it's too early for him to judge his season.
"It's not over; I mean, you know me," Jeter said. "We're trying to win games. We've lost these first two here. That's the only thing I'm thinking about -- trying to win today. Those other things, I don't let them enter my mind."
Jeter has bristled at the suggestion that he needed to prove people wrong after enduring a down 2010 campaign that featured some career-low numbers.
"I hit .270, man. You know?" Jeter said. "Sorry. One time I hit .270, and it's like it was the end of my career. You're going to struggle. You're going to have good years, you're going to have bad years. But you always have to have confidence that you can play."