HOLLAND, Michigan (Reuters) - Republican Mitt Romney said on Tuesday his White House campaign was vetting U.S. Senator Marco Rubio of Florida as a potential vice presidential pick, denying a report that Rubio was not being seriously considered as his running mate.

"The story was entirely false, Marco Rubio is being thoroughly vetted as part of our process," Romney told reporters outside an ice cream shop in Holland, Michigan, as he wrapped up a five-day, six-state bus tour of battleground states.

It was the first time Romney has publicly acknowledged exploring the background of a potential Republican vice presidential pick during what has been an almost entirely secret process.

Romney has routinely refused to discuss individual candidates who might join him to face the Democratic ticket of President Barack Obama and Vice President Joe Biden in November's election.

Romney's comments followed an ABC News report that his campaign was not vetting Rubio, a fast rising conservative star in the party, for the No. 2 slot. A serious vetting would typically involve looking into financial and personal records of the candidate.

"There are only two people in this country who know who are being vetted and who are not. That's Beth Myers and myself, and I know Beth well, she doesn't talk to anybody," Romney told a small pool of reporters who were brought to the ice cream shop to hear his statement.

Myers is a confidant and adviser to Romney, the former governor of Massachusetts.

Rubio is a Cuban-American who has been touted for his ability to help Romney appeal to Latinos. Ruling him out as even a potential candidate would risk further alienating a growing voting bloc that has been unhappy with Romney's hardline immigration stance.

(Reporting by John Whitesides; Editing by Jackie Frank)