Sen. Jeff Sessions of Alabama says he is open to serving as Donald Trump's running mate, describing it as a potential opportunity to work in a "historically positive administration."

The 69-year-old Republican, currently in his fourth term, made the rare acknowledgement of interest in a higher office to U.S. News in an interview on Thursday, stressing that he has had no conversations with the Trump campaign about the vice presidency.

"I would have no objection to serving in a Trump administration, but I'm not pushing for that. I'm not expecting it to happen, but I don't want it being reported that I wouldn't take and wouldn't consider serving in a Trump administration because I think it could be a historically positive administration," Sessions says.

Sessions, who became the first sitting U.S. senator to endorse Trump back in February, is the New York billionaire's chief liaison on Capitol Hill. He speaks to Trump several times a week by phone, including on Thursday morning before Trump clinched the 1,237 delegates officially needed to become the presumptive Republican presidential nominee.

Sessions was drawn to Trump by his hard-line immigration stance and pledge to erect a wall on the Mexican border, as well his blistering critique of American trade deals that both men believe have hollowed out the country's manufacturing sector and sucked away jobs.

Though he demurred when asked whom he thought would make a smart running mate for Trump, Sessions said that on balance, a governing partner is more critical than a choice based on electoral significance.

"The best politics and the best substance is to try to get the best person you can get, somebody who would be a good president. The people will see that – somebody you trust and feel like you could work with and somebody who can help you govern," Sessions says. "[President John] Kennedy and [Vice President Lyndon] Johnson apparently never got along very well. It's better if you get along with your vice president."

Trump has assembled a preliminary, malleable list of potential vice presidential selections, which includes Tennessee Sen. Bob Corker, retired Lt. Gen. Michael Flynn, former Speaker of the House Newt Gingrich and Sessions. Advisers say Trump's goal is to unveil his selection the week of the Republican National Convention in July, but there's no indication a formal vetting process is underway.

"I've never talked to him about anything for me," Sessions says. "He'll decide who he wants to pick. It is a big thing and it does need to be done right."

Sessions says he is not intensely lobbying his GOP Senate colleagues to embrace Trump, instead choosing to provide them with information that may allay their concerns or bolster his candidate's case.

For instance, in conversations with Republican lawmakers, Sessions says he often points out that conservative economists like Larry Kudlow and Stephen Moore have embraced Trump's tax plan. It's a way to explain how Trump is more ideologically in sync with party doctrine than many on the right believe.

"I think Trump is right down the alley with them," Sessions says. "If you look at his agenda, it's something we all ought to be able to support. The Republican Party can support this agenda. They may not like some of his expressions and aggressive talk and may feel some of his criticisms are exaggerated and unfair, but fundamentally, it's fair."

Sessions says he was heartened after one GOP senator recently told him he would issue a strong statement of support when Trump landed in his state. The downside: The senator, whom Sessions declined to name, would be out of the country at the time.

Sessions also seemed to wrestle with just how critical party unity will be going forward for Trump.

"It's less important this year than probably ever before, but I think it's important," he says. "How many endorsements did [Jeb] Bush have? One hundred and sixty or something? I mean, the people with the most endorsements went down the fastest. Their endorsements didn't provide very much other than an indication that this person was a product of what the voters think is the problem."