Still, Noem said that Trump would send a powerful message by choosing a woman as his vice president.

“I just feel like whenever you have a woman at the table, you have a better perspective on every single issue. Women are the majority of the voters in this country. Whenever I’ve been in a discussion where women and men are at the table, I feel like it’s more rounded. It’s more collaborative,” Noem said. “So I think it would bring a lot to his ticket if he were able to do that.”

There are a number of prominent Republican women who could land on Trump’s short list. Lummis floated former Secretary of State Condoleezza Rice and Sen. Kelly Ayotte (R-N.H.) as possibilities.

Ayotte is considered one of the most vulnerable Senate Republicans up for reelection in November, but it’s unclear whether she’d be open to running with Trump. She has not endorsed any candidate in the GOP primary but has said she will support the eventual nominee.

“Kelly is focused on doing her job serving the people of New Hampshire in the Senate, and she is running for reelection,” Ayotte campaign spokeswoman Liz Johnson said in response to the vice presidential idea.