Romney said Monday that Beth Myers is in charge of "selection and vetting and analysis."
"I have selected someone who has been a counselor of mine for a number of years, Beth Myers. She was my chief of staff when I was governor," Romney said during an interview with Diane Sawyer of ABC News outside Fenway Park in Boston.
Romney is moving forward as the presumptive Republican presidential nominee after rival Rick Santorum suspended his campaign last week.
Myers was Romney's chief of staff when he was Massachusetts governor. She currently is a senior adviser on his presidential campaign.
When asked about Florida Sen. Marco Rubio, Romney said "he's one of the terrific leaders in our party."
"But I think it's way too early to begin narrowing down who the potential vice presidential nominees might be," he said. "But we're beginning that process, we'll talk about a lot of folks, and then go through the kind of vetting and review process that you have to go through to make sure whoever you select will pass the evaluation that's required by the American people."
Romney wouldn't offer any hints as to when the months-long process would end.
"We do have a deadline in mind as to when I'd like to be able to reach a decision but I'm not giving you that date at this stage," he said in the interview, adding that it would "certainly" happen before the Republican National Convention in late August.