Welcome to VP Watch, NBC's roundup of the latest news about each presumptive nominee's search for a running mate.

Top Headlines: The GOP

Donald Trump tweeted plaudits to three potential VP picks on Monday — Sens. Tom Cotton and Joni Ernst, as well as Indiana Gov. Mike Pence. Cotton and Ernst are rising GOP stars and, it’s worth noting, both vice-chairs of the NRSC who are involved in helping elect Republicans to the Senate. He praised Cotton for the senator's appearance on Meet the Press this weekend; said he was “very impressed” by his meeting with Pence; and announced a surprise meeting with Ernst that a source tells NBC News’ Kasie Hunt was “very last-minute." He also dismissed those who aren't in the running.

The only people who are not interested in being the V.P. pick are the people who have not been asked! — Donald J. Trump (@realDonaldTrump) July 4, 2016

Top Headlines: The Democrats

1) You know you’re in full #veepstakes season when four of Hillary Clinton’s potential running mates made the Sunday show rounds to continue their auditions for the role. Ohio Sen. Sherrod Brown, New Jersey Sen. Cory Booker, California Rep. Xavier Becerra, and Labor Sec. Tom Perez were all grilled on one of the network Sunday shows (Tim Kaine was on Meet The Press last week). All the potential running mates seemed to give the same answer when asked if they were being vetted by Clinton’s team — referring those questions to the Clinton campaign instead.

Tom Perez, Elizabeth Warren, Xavier Bercerra, Cory Booker, Sherrod Brown and Juilo Castro

2) Just as a number of President Obama’s cabinet members have been making the Sunday show rounds and appearing at political events with Clinton, the Obama administration has moved to prohibit all cabinet members from speaking at the Democratic National Convention this month, via the New York Times.

3) Check out our piece on what Hillary Clinton would get with a VP pick of Tim Kaine, one of her frontrunners.

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More VP News: The GOP

NEWT GINGRICH: Newt & Callista Gingrich took to the golf course at the Aspen Golf Club on Monday after attending the Aspen Ideas Festival over the weekend, where Gingrich spoke for an hour about the state of American politics and addressed his vetting for the VP slot. Gingrich insisted he had still yet to speak with Trump specifically about joining the ticket, and Gingrich told NBC News that “like is a pretty strong term” to describe whether he’d like to be Trump’s pick. He said that being the running mate "really messes up your life,” and then suggested he’d “really like” to be an “outsider adviser” to the potential administration, like he did for the George W. Bush White House.

For an individual being actively vetted, Gingrich’s critiques of Trump were sharp. He said it’s Trump’s job to “quit screwing up” and said he wished Trump would “cut off the last 10 percent” of what he says. And Gingrich expressed that Trump -- to pass appointments and legislation -- would have “a huge problem” if he is “not dancing” with Senate Majority Leader Mitch McConnell, who just last week refused to call his party’s presumptive nominee “qualified” for the job.

MIKE PENCE: Mike Pence told reporters in Indiana this weekend that “nothing was offered” during his meeting with Trump on Saturday, but described it as a “fun” meeting. The governor said Donald Trump and his wife Melania met with him, his wife and his daughter and were “gracious and kind” to the family, and that the two Republicans ”talked about our country [and] the progress we’ve made in Indiana.” Trump tweeted his praise for the Indiana governor on Sunday. Still, Pence wouldn’t wade into the latest controversy dogging Trump, refusing to answer multiple questions about the controversial image Trump tweeted over the weekend, and he wouldn’t say whether he’d take the VP spot if offered. Pence walked in two Independence Day parades on Monday, where shouts of “VP” were numerous along the sidewalks.

Tom Cotton, Mike Pence, John Thune, Bob Corcker, Joni Ernst and Newt Gingrich

BOB CORKER: Corker has remained quiet in recent days, but on Friday, a Yahoo Finance report detailed how Corker & Sen. Mark Warner of Virginia profited millions off an investment into a fund that bet against the real estate market and subsequent housing crash. Corker’s payout, per the report: "From 2006 to 2014, he reported total income from Pointer of between $3.9 million at the low end and $35.5 million at the high end (including funds from the sale of part of his stake in the fund in 2012.) He sold the rest of his stake in 2014 and reported a cash receivable from Pointer of between $5 million and $25 million that year."

This report follows a WSJ story in May that detailed a FBI investigation into accounting fraud by a real estate company based in Chattanooga that Corker has made millions off of in stock investments.

In a statement, Corker spokesman Micah Johnson said "This is yet another ridiculous narrative being peddled by a politically-motivated special interest group that refuses to disclose its donors. This dark money entity has an abysmal track record for accuracy, and just like the other unfounded claims they have leveled against Senator Corker, this too is completely baseless."

JONI ERNST: Though speculation about her as a vice-presidential shortlister had died down in recent weeks, the presumptive GOP nominee tweeted Monday that he’d be meeting with her in New Jersey. A source close to Ernst told NBC News’ Kasie Hunt that the meeting came as a surprise and was planned “very last-minute.” In a statement to NBC News, Ernst said she "had a good conversation with Donald Trump today and we discussed what I am hearing from Iowans” during her travels around the state. Ernst, a retired lieutenant colonel in the Iowa Army National Guard, also said she’d 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."

JOHN THUNE: He's attending the 155th Engineer Company's welcome home ceremony from a deployment in Kuwait Monday in Rapid City.

TOM COTTON: In an interview on “Meet the Press” this Sunday he seemed to indicate he had little interest in the job. He railed against Hillary Clinton’s foreign policy experience and policies, but offered little praise for Trump, even declining to make a positive case for why Trump is the better candidate. "Donald Trump can ultimately make the case for himself," he said. Still, the presumptive GOP nominee tweeted his praise for Cotton on Monday, saying that "Despite a totally one-sided interview by Chuck Todd, the end result was solid!"

More VP News: The Democrats

TIM KAINE: NBC's Kailani Koenig traveled to Richmond to take a look at some what Clinton has to consider in Tim Kaine as a running mate, from his position as a more traditional pick in a very untraditional year, to his time in Richmond, his faith, and the map in Virginia, and more. On Tuesday, Kaine will host a roundtable discussion in Richmond with Virginia health officials about Zika preparedness, and then head back to DC again as the Senate is back in session this week.

SHERROD BROWN: Brown referred any questions about the VP vetting process to the Clinton campaign when asked on ABC’s “This Week” on Sunday, declaring, “I’m simply not going to speculate on that. I love the job that I get to do.” He also predicted that Clinton will not be indicted over her use of a private email server as secretary of state, and he called former President Clinton’s meeting with Loretta Lynch “unfortunate.” Brown also threw barbs at Trump over trade, and defended Clinton’s past comments on the TPP before she came out against it, saying, “it was her boss.”

Tuesday, Brown will visit a summer feeding site in Akron, Ohio where children can receive free meals through the Summer Food Service Program (SFSP) as he works to raise awareness about the program.

ELIZABETH WARREN: There’s another piece, this time from the Washington Times, on why a Clinton-Warren ticket won’t automatically lock in all of Bernie Sanders’ supporters. Her speech last week on wanting to crack down on tech giants Apple, Google, and Amazon continues to make headlines.

JULIAN CASTRO: Not much new from Castro as he is home for the weekend in Texas, other than a piece from ABC about how he is being vetted — which NBC has already confirmed — and what he could potentially bring to a Clinton ticket.

XAVIER BECERRA: Becerra went on Fox News Sunday, deferring to the Clinton campaign when asked if he’s being vetted for the VP job, saying, “that's a question that has to be asked of Secretary Clinton,“ adding that she has a lot of qualified people to choose from — “we’ll see, we’ll see," and also acknowledging that Clinton "understands that she's got to earn people's trust."

SECRETARY TOM PEREZ: Perez was grilled on Meet The Press on Sunday, where he kept slamming Donald Trump as a “fraud" and then gave some pretty vague answers to some basic foreign policy questions. He also reaffirmed that he’s “proud” of his work on the TPP trade deal, a a deal that separates him from Clinton. Watch the full interview.

CORY BOOKER: Booker is also now directing questions about whether he is being vetted to the Clinton campaign, he said in an interview on CNN’s “State of the Union” Sunday. Booker is spending the whole weekend around the NY/NJ area, went hiking with some Boy Scouts and Girl Scouts, marched in a 4th of July parade in Paramus and attended a naturalization ceremony in Jersey City.