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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 RubioRubio defends Trump: 'This whole flip-flop thing is a political thing' Rubio: Shutdown would have 'catastrophic impact' on global affairs Sunday shows preview: Trump stares down 100-day mark MORE (Fla.) and Rob PortmanRob PortmanFive things to know about Trump's steel order Mexico: Recent deportations 'a violation' of US immigration rules EPA union asks Pruitt for meeting over talk of closing office MORE (Ohio), and Rep. Paul RyanPaul RyanFive fights for Trump’s first year Sunday shows preview: Trump stares down 100-day mark Ryan: Focus is on keeping government open, not healthcare 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.