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"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 Cybersecurity: Bipartisan bill aims to deter election interference | Russian hackers target Senate | House Intel panel subpoenas Bannon | DHS giving 'active defense' cyber tools to private sector Senators unveil bipartisan push to deter future election interference Puerto Rico's children need recovery funds MORE (Fla.) and Rob PortmanRobert (Rob) Jones PortmanFlake's anti-Trump speech will make a lot of noise, but not much sense Top GOP candidate drops out of Ohio Senate race Overnight Tech: Regulators to look at trading in bitcoin futures | Computer chip flaws present new security problem | Zuckerberg vows to improve Facebook in 2018 MORE (Ohio), and Rep. Paul RyanPaul Davis RyanGOP leaders pitch children's health funding in plan to avert shutdown Lawmakers see shutdown’s odds rising Fix what we’ve got and make Medicare right this year 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.