Ms. Ernst is a retired National Guard lieutenant colonel and a veteran of the Iraq war. Her military background could help Mr. Trump given his lack of foreign policy experience or national security experience. The fact that she is a woman could also help Mr. Trump with a group of voters with whom he currently polls poorly.

Ms. Ernst is also considered a possible keynote speaker at the Republican National Convention, which begins on July 18 in Cleveland.

In the statement, Ms. Ernst said that her focus was on defeating Hillary Clinton, saying, “I had a good conversation with Donald Trump today, and we discussed what I am hearing from Iowans as I travel around the state on my 99-county tour, and the best path forward for our country.”

She added: “I will continue to share my insights with Donald about the need to strengthen our economy, keep our nation safe and ensure America is always a strong, stabilizing force around the globe.”

According to a source briefed on the meeting, both Paul Manafort, Mr. Trump’s chief strategist who is handling much of the vice presidential search, and Reince Priebus, the Republican National Committee chairman, also attended.