The senator, who is not running for reelection to his Senate seat, also told interviewer Jake Tapper that he's not interested in serving as Trump's running mate.
"He won the nomination, and he deserves to have a running mate that more fully embraces some of the things he stands for," Rubio said.
He said his "policy differences with Donald Trump" are well known.
"That said ... I don't want Hillary Clinton to be president. If there's something I can do to help that from happening, and it's helpful to the cause, I'd most certainly be honored to be considered for that," Rubio said.
Rubio ended his presidential bid in March after losing by a wide margin to Trump in Florida. He amassed 165 delegates in his quest for the presidency and took the unusual step after dropping out of the presidential race of asking states not to release those delegates.
But now, he tells CNN, "basically we technically have already" released the delegates, so they should vote for Trump. That means GOP delegates across the country — in Alabama, Alaska, Arkansas, Georgia, Minnesota, the District of Columbia, Puerto Rico and elsewhere — can join the majority of other delegates from across the country and vote for Trump on a first ballot in Cleveland.
In the months since returning to the Senate, Rubio has turned mostly to home-state concerns, including the growing threat of the Zika virus and federal oversight of a poorly managed housing project in Jacksonville. But he has also stoked speculation about his future by sitting for a series of interviews that invite questions on the subject. Insisting that he plans to be a private citizen next year, he has revived his relationship with D.C. super-lawyer Robert Barnett to explore his post-Senate options.
Rubio's comments to CNN aired on the same day that Republican senators reportedly began pressuring him to reconsider his decision not to seek reelection to the Senate. Currently, five Republican contenders are vying to succeed Rubio in what promises to be a messy, expensive primary fight while Florida Democrats are poised to coalesce around Rep. Patrick Murphy, who has raised millions of dollars for his bid. With 24 seats to defend this year, Republican leaders are hoping to avoid spending tens of millions of dollars to back a candidate in Florida.
In response to the overtures, Rubio told reporters on Thursday that it's "unlikely" he would launch a reelection campaign. For those who've tracked the trajectory of Rubio, those comments signal that the door has opened, even if just a little bit.
It's a "safe assumption" that he'll run for office again someday, Rubio told CNN, reiterating comments he has made in similar interviews.
"I can tell you I enjoy public service. If there's an opportunity to serve again in a way that I feel passionate about, I'll most certainly think I would explore it," the senator said. "But I don't know where I'm going to be in two years. I don't know what my life will look like then."
In two years, Florida will be holding a gubernatorial election, and the state's senior senator, Democrat Bill Nelson, may opt to retire — potentially opening up two opportunities for Rubio.