Politico, a Washington publications, said Thursday that three unidentified sources said Rove personally contacted the Lieberman to ask him to withdraw from the pool of potential running mates for presumptive Republican Party presidential candidate John McCain, a U.S. senator from Arizona.

The sources alleged that during Rove's phone call last week, Lieberman dismissed the strategist's request.

"Rove called Lieberman," one of the sources told Politco. "Lieberman told him he would not make that call."

While Rove has no official role in McCain's presidential campaign, he remains close to many of the top officials involved with the presidential hopeful's campaign.

Politico said Rove has tabbed former Massachusetts Gov. Mitt Romney as the best choice for McCain's running mate during the general election.

"Romney is already vetted by the media, has strong executive experience both in business and in government, has an interesting story to tell with saving the U.S. Olympics, and also helps McCain deal with the economy, because he can speak to the economy with a fluency that McCain doesn't have," Rove said in June.