The survey by Fairleigh Dickinson University's PublicMind asked registered GOP and independent voters to name their preferred vice president for the GOP ticket, offering no suggestions but asking the open-ended question: "No matter who is the Republican nominee for president, if you could pick the vice presidential nominee who would it be?"

Rubio took the top spot, with 8 percent of those surveyed giving his name. He was followed by former Pennsylvania Sen. Rick Santorum with 7 percent and New Jersey Gov. Chris Christie with 6 percent.

Rubio, who has not endorsed in the primary, has been named by all of the GOP candidates for their likely-VP shortlist, but he has said he is not interested. Christie, who endorsed Mitt Romney, has also dismissed the possibility of appearing on a ticket. 

Santorum remains a front-runner in the GOP race.

The poll was conducted from Feb. 6 to Feb. 12 and has a 3.5 percent margin of error.