Donald Trump on Monday spent part of his July 4th with Sen. Joni Ernst -- fueling speculation that the Iowa freshman senator could be on the short list of his vice presidential picks.

Ernst told Fox News they had a "good conversation," adding, "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."

Earlier, Trump tweeted, "I look forward to meeting (Ernst) today in New Jersey. She has done a great job as Senator of Iowa!"

Over the weekend, Trump met with Indiana Gov. Mike Pence and his wife, though a Pence spokesman said "nothing was offered."

The spokesman, Marc Lotter, added, "The governor had warm, productive meetings with the Trumps." He declined to say where the Saturday meeting was held. Pence is running for re-election against Democratic former state House Speaker John Gregg.

Trump and Pence discussed Pence's policies during his term as governor which began in 2013, Lotter said. He also declined to discuss Pence's level of interest in the position, echoing a comment from Pence last week that he did not want to talk about "a hypothetical."

Trump tweeted Monday about his Saturday meeting with Pence.

"Spent time with Indiana Governor Mike Pence and family yesterday. Very impressed, great people!” Trump tweeted.

As Pence and his wife arrived for a concert Sunday night at Conner Prairie, a history park in Fishers, the governor again declined to discuss whether he was interested in the position. He reiterated his support for Trump's candidacy and said the Trumps "couldn't have been more kind and gracious" during the meeting.

Trump has never held public office and is considering a small group of political veterans as potential running mates.

People with direct knowledge of Trump's vetting process say the list includes Pence, former House Speaker Newt Gingrich, New Jersey Gov. Chris Christie and Alabama Sen. Jeff Sessions.

In addition to serving as governor, Pence served in the U.S. House of Representatives for 12 years.

He also at one time had his own presidential ambitions but last year ruled out a run after his popularity fell in the wake of criticism over his handling of the state's religious objections law.

Fox News' Chris Snyder and The Associated Press contributed to this report.