Very well-placed sources told FOX News late Monday that John McCain's campaign has had discussions recently about the merits of the expected Republican presidential nominee unveiling his choice of a running mate this week while rival Barack Obama is overseas.

One source with direct knowledge of the senator's thinking and of the campaign's machinations said no announcement will be made Tuesday morning but another top insider suggested the media not throw cold water on the idea that McCain could announce his vice presidential pick this week. Still a third source said unless McCain wakes up in the next two days with a decision, chances are "remote."

Asked about the odds of announcing a vice presidential pick on Tuesday, McCain brushed off the question during a plane ride with reporters to New Hampshire, giving only a mischievous grin.

McCain told reporters that he wants to make a choice as early as possible and make sure that the person doesn't detract from that ticket. He separately noted onetime rival Mitt Romney's success in his native Michigan, a battleground state in which the former Massachusetts governor beat McCain by 9 points.

But traveling Press Secretary Brooke Buchanan said no announcements would be made late Monday. Senior adviser Mark Salter said he had "no comment and he is not authorized to say anything" regarding the No. 2 pick."

The speculation prompted by the suggestion takes some of the spotlight off Obama's foreign trip, meant to showcase the Democrat's gravitas on national security issues. Diverting the focus is a big part of the McCain camp's goal this week. Senior McCain aides went behind closed doors most of Monday afternoon and were out of pocket throughout the night.

McCain has scheduled a meeting of his kitchen cabinet in his hometown of Sedona, Ariz., this weekend to lay out the path ahead for top national campaign leaders and surrogates.

In the past, such events have included various vice presidential short-listed names, including Romney, former Arkansas Gov. Mike Huckabee, Louisiana Gov. Bobby Jindal, former Office of Management and Budget Chief and Ohio Rep. Rob Portman, South Carolina Sen. Jim DeMint, Minnesota Gov. Tim Pawlenty, former Homeland Security Secretary and Pennsylvania Gov. Tom Ridge, South Carolina Gov. Mark Sanford and Independent Democratic Sen. Joe Lieberman.

Speculation has focused on Romney in recent weeks, but contrary to reports that Romney will join McCain in New Orleans on Thursday, his aides say he is on vacation in Ontario and has had no invitations to join McCain this week.

Click here to read more from FOX News' Shushannah Walshe on the vice presidential talk on the campaign trail.

FOX News' Carl Cameron and Shushannah Walshe contributed to this story.