The IBOPE Inteligencia poll found 22 percent of overall voters prefer Rubio to be Romney's running mate, including 36 percent of Republican voters.
The poll gave respondents a choice between 12 possible candidates, of whom only Rubio drew more than 10 percent of the vote. Louisiana Gov. Bobby Jindal received 8 percent and U.S. Rep. Paul Ryan of Wisconsin received 7 percent.
The poll found 44 percent of voters said the Republican vice presidential nominee should be a moderate with an established public service record, while 15 percent said Romney's running mate should be someone with a small public service record who will attract votes from particular groups.
Twenty-eight percent of respondents were unsure who they wanted, and 14 percent wanted someone else. The poll also found 73 percent said Romney's choice of running mate will not influence their vote, 6 percent said it will have a large influence and 18 percent said it will have some influence.
IBOPE Inteligencia surveyed 2,071 people online from June 22-25. The margin of error was 2.2 percentage points.