"I don't think she'd want to do it," Trump said, although he added that he isn't thinking that far ahead.
Appearing on NBC's "Today" show on Wednesday morning after Palin's high-profile endorsement of his White House bid, Trump deflected repeated questions about the 2008 vice presidential candidate as a potential 2016 running mate.
"She's been through that," he said.
Palin has not raised the matter with the GOP frontrunner.
"As far as Sarah is concerned, never asked me about that, never asked me about anything else, just wanted to support," Trump said.
"You know, I really don't get into it right now. That question is always asked to me, who do you have in mind, and I don't even think about VP right now," he said. "I just want to win. I've always been a closer."
But Trump said Palin could certainly be a part of his administration.
"Certainly there would be a role somewhere in the administration, if she wanted -- and I'm not sure that she does want that -- but there would certainly be a role."
Palin told CNN's Jake Tapper last September she might be interested in becoming energy secretary.
Trump also touted the significance of Palin's endorsement.
"Every candidate wanted Sarah, I mean, everybody," he said. "They all respect her a lot. So many people are disappointed that she didn't support them."