Donald Trump tweeted Monday he would spend part of his July 4th with Sen. Joni Est -- fueling speculation that the Iowa senator could be on the short list of his vice presidential picks.

"I look forward to meeting (Est) today in New Jersey. She has done a great job as Senator of Iowa!" Trump tweeted about the freshman lawmaker. There was no immediate response from Est.

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 goveor 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 goveor 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.

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"Spent time with Indiana Goveor 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 goveor 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 goveor, 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.

The Associated Press contributed to this report.