"I look forward to meeting @joniernst today in New Jersey. She has done a great job as Senator of Iowa!" Trump tweeted early Monday.
Ernst's name appeared in reports on VP shortlists over the weekend,
and a senior Trump adviser confirmed to CNN that Ernst is being considered.
After the meeting on Monday, Ernst said she had "a good conversation with Donald Trump."
"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 said in a statement. "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."
Trump also doled out some conspicuous praise for Indiana Gov. Mike Pence and Arkansas Sen. Tom Cotton, who have also been floated as potential running mates.
Trump tweeted his approval of Cotton's performance in an interview on Meet the Press on Sunday: "Senator Tom Cotton was great on Meet the Press yesterday. Despite a totally one-sided interview by Chuck Todd, the end result was solid!" Trump wrote.
In the interview on NBC,
Cotton discussed his support for Trump, but when asked to explain why he should be president, the Arkansas senator said only that "Donald Trump can ultimately make the case for himself." Pressed on why his support seemed less than full-throated, the hawkish Arkansas freshman jokingly offered that "maybe I just don't demonstrate enthusiasm much in life, especially in such dangerous times as these."
And Trump complimented Pence, whom he met with Saturday, writing, "Spent time with Indiana Governor Mike Pence and family yesterday. Very impressed, great people!"
Marc Lotter, a spokesman for Pence, described the meeting as "warm and friendly" in a statement. Nodding at the vice presidential speculation, he also said that "nothing was offered and nothing was accepted."
Pence endorsed Sen. Ted Cruz of Texas ahead of the Indiana primary back in May, but did not come out strongly against Trump.
Trump, apparently aware of the speculation surrounding the pick, capped the series of tweets with a pointed sign-off: "The only people who are not interested in being the V.P. pick are the people who have not been asked!"