Republican Texas Gov. Greg Abbott was recently floated as a potential vice presidential pick for former President Donald Trump, but he seemingly shot down that idea during a Tuesday interview, according to The Hill.

Abbott made it clear that while he appreciated the consideration as a prospective running mate for the likely Republican presidential nominee, he was instead closely focused on seeking re-election for another term as governor of the Lone Star state.

Gov. Abbot "absolutely" a contender to be Trump's VP

The Hill reported separately last week that former President Trump himself acknowledged that Gov. Abbott was on his "short list" as a possible vice presidential pick while visiting with the governor during a trip to the southern border with Mexico.

During an interview on Thursday with Fox News host Sean Hannity, while seated alongside Abbott, Trump was asked by the host if the governor was among the list of potential running mates under consideration, to which the former president replied, "Absolutely, he is."

Trump and Abbott are quite clearly aligned when it comes to their oft-stated desire to fully secure the nation's southern border with strict enforcement of existing laws that deal with illegal immigration, which has spiraled out of control to record-setting levels under current President Joe Biden.

Continuing to govern Texas "truly is my focus"

On Tuesday, Gov. Abbott appeared for an interview on NBC News and was asked at one point about being mentioned by former President Trump as a possible running mate and whether he would accept a hypothetical offer from the likely GOP nominee to be the vice presidential candidate.

"So listen, he’s very kind in suggesting things like that," Abbott said of Trump mentioning him as a contender for the VP slot.

"One thing that I’m deeply committed to, and that is governing the great state of Texas," he added. "I’ve already announced I’m running for reelection. And that truly is my focus."

Sen. Tim Scott earned another mention as a top contender

The prior report from The Hill noted that in addition to Gov. Abbott, former President Trump also mentioned Sen. Tim Scott (R-SC) as a top contender to be his running mate during the interview with Fox News host Hannity.

That is now the second time that Trump has specifically highlighted the South Carolina senator as being on his "short list" of prospective VP candidates, as he offered up high praise of Scott during a town hall event last month with Fox News host Laura Ingraham.

Ingraham had rattled off a list of names provided ahead of time by audience members of who they'd like to see Trump pick as his running mate, and that list included in addition to Scott prominent names like business entrepreneur Vivek Ramaswamy, Florida Gov. Ron DeSantis, South Dakota Gov. Kristi Noem, Rep. Byron Donalds (R-FL), and former Rep. Tulsi Gabbard (D-HI), a former Democrat turned independent.

Trump told Ingraham that all of the names she mentioned were individuals that he was strongly considering to be his vice presidential candidate.

The Hill observed that other likely contenders for the position who weren't mentioned by Ingraham but have nonetheless been floated as possibilities in other discussions included House Republican Conference Chair Elise Stefanik (R-NY), Sens. J.D. Vance (R-OH) and Katie Britt (R-AL), and former White House press secretary turned Arkansas Gov. Sarah Sanders, among others.