(CNN) Donald Trump on Tuesday said Alabama Sen. Jeff Sessions is "certainly someone I would consider" for his vice presidential running mate.

Speaking at a news conference in Trump Tower in New York, Trump called Sessions -- who in February became the first sitting senator to endorse Trump -- a "fantastic person" who would "absolutely" be looked at for the No. 2 spot on the ticket.

Sessions, a fourth-term senator who is helping craft Trump's national security policy, has called for the Republican Party to coalesce behind Trump, lobbying his fellow senators and even House Speaker Paul Ryan to endorse Trump.

The Alabama senator said during a taping of Politico's "Off Message" podcast that Ryan "needs to recognize, on some of these issues, Trump is where the Republicans are and if you're going to be a Republican leader, you should be supportive of that."

He added, "I think the leaders in all parties tend to adjust to reality. They just have to or they won't remain in office...Already, many are sensing it."

Earlier this month, Sessions told CNN that it would be an "honor" to serve as Trump's VP. He told US News and World Report on Sunday, however, that he has "never talked to" Trump about serving in his administration and that in the end Trump will "decide who he wants to pick."

"It is a big thing and it does need to be done right," Sessions added.

Trump has narrowed his potential running mates to a "very small" list, his top aide said Sunday

In an appearance on "Fox News Sunday," Trump campaign manager Corey Lewandowski -- who is leading the vice-presidential search process -- said the vetting team has "started to shrink down that pool."