Many Republicans believe Romney will break from tradition and announce his choice well before the party's convention in Tampa in late August that will formally nominate Romney as the Republican candidate.
Still, Romney, the former Massachusetts governor, has yet to make up his mind.
Naming his vice presidential running mate in coming days could help Romney remove a withering spotlight instigated by the Obama campaign over his personal financial information and tenure at the private equity firm Bain Capital.
The Democrats accuse Romney of leading Bain at a time when it invested in companies that outsourced U.S. jobs overseas. Romney says he was running the Winter Olympics in Salt Lake City at the time and had given up all management of the company.
The controversy is proving to be a distraction for the Romney campaign and overshadowing his attempt to make the election campaign about Obama's handling of the U.S. economy amid 8.2 percent unemployment and record budget deficits.
Reuters say he has yet to make up his mind
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The short list includes Ohio Senator Rob Portman, former Minnesota Governor Tim Pawlenty and Louisiana Governor Bobby Jindal all offering various strengths to Romney.
Fox News Latino reports that Romney's short list is down to two not including Marco Rubio of Florida, or Gov. Susana Martinez of New Mexico.