"I'd love that because she really is somebody that knows what's happening and she's a special person," the Republican candidate said on "The Palin Update," an online interview show. "She's really a special person and I think people know that."
Trump didn't say whether he would consider Palin for a Cabinet-level post or some other role, but told host Kevin Scholla that she has "a following that's unbelievable." Palin's fans, he added, are always urging him to "get Sarah's support."
Trump also said that he and Palin have something in common.
"Like me, she's got people that don't exactly love us and we understand who they are and sort of forget about that," Trump said. "But she has a tremendously loyal group of people out there for her."
Palin, who is highly active on social media, has not yet responded to the overture. However, she has praised Trump in the past.
"Trump is the candidate giving voice to untold millions of fed-up Americans witnessing a purposeful destruction of our economy and the equal opportunity for success that made America exceptional," Palin wrote on Facebook last week.
"The Palin Update" is part of Mama Grizzly Radio, a website dedicated to the 2008 GOP vice presidential nominee and the issues she raised.