"But I'm going to do everything I can to help him in Virginia,” he promised.

McDonnell has been less vehement in his denials about being considered for the vice president position in comparison to other frequently mentioned names, such as Indiana Gov. Mitch Daniels and South Carolina Gov. Nikki Haley.

McDonnell, who is restricted by state law from seeking a second consecutive term as governor, told Fox News earlier this month that he would “consider” the possibility if asked.

“Any candidate that calls a potential nominee and says, 'Listen, you can help the party; you can help the country' — of course you would consider it," McDonnell said. "I’m not asking for it. I’m not interviewing for it. I just want to see Mitt Romney win.”

Romney put Beth Myers, a long-time member of his political team, in charge of running the search and vetting process for his vice presidential nominee. Myers has already begun contacting potential running mates, according to reports.

Other likely possibilities on the short list — Sens. Marco RubioMarco Antonio RubioOvernight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Trump bets base will stick with him on immigration MORE (Fla.) and Rob PortmanRobert (Rob) Jones PortmanWeek ahead in tech: Debate over online sex trafficking bill heats up 'Hillbilly Elegy' author won't run for Senate Brown, Portman urge Trump administration to move quickly on a steel decision MORE (Ohio), and Rep. Paul RyanPaul RyanRyan: Graham-Cassidy 'best, last chance' to repeal ObamaCare Ryan: Americans want to see Trump talking with Dem leaders Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE (R-Wis.) — all declined to talk about whether they'd been contacted by the campaign when The Hill asked them earlier in May.

The election is expected to hinge on swing states like McDonnell’s. Virginia went to President Obama by 6 points in 2008, making him the first Democrat to win the state in a presidential election since 1964.