By Amanda Becker

WASHINGTON (Reuters) - Democratic U.S. presidential candidate Hillary Clinton's campaign is vetting retired Navy Admiral James Stavridis as a potential vice presidential running mate, a source with knowledge of the process told Reuters on Tuesday.

Stavridis is dean of the Fletcher School of Law and Diplomacy at Tufts University near Boston and a former supreme allied commander of NATO.

"Admiral Stavridis is one of the finest military officers of his generation," Michele Flournoy, a former under secretary at the U.S. Department of Defense, told Reuters in a statement.

"He is a person of great ability and integrity, and an exceptional leader. He has the talents, experience, judgment and temperament to serve the American people at the highest levels of our government."

The Clinton campaign declined to comment on the vetting of Stavridis. Stavridis likewise declined to comment on the process.

Flournoy, who formed a think tank after leaving the Defense Department and is advising the Clinton campaign on foreign policy, also did not comment on the vetting process.

Flournoy is thought to be a probable Clinton pick for defense secretary if the presumptive Democratic nominee wins the White House on Nov. 8.

Stavridis and Clinton worked closely together when he was at NATO and she led the U.S. State Department during Democratic President Barack Obama's first term.

Introducing Clinton at a 2013 awards dinner, Stavridis said, "She does the work of two, of 20, of 200 with her energy, with her enthusiasm and with her boundless determination to improve our world," and praised her use of "smart power."

In a 2012 TED talk on global security, Stavridis began by saying: “My thesis for us today is, instead of building walls to create security, we need to build bridges."

Clinton has used similar rhetoric about the role of international diplomacy on the campaign trail.

Stravidis was senior military assistant to former Defense Secretary Donald Rumsfeld in the George W. Bush administration during the early years of the U.S. occupation of Iraq. That could provide presumptive Republican presidential nominee Donald Trump with a line of political attack.

Trump has throughout the campaign criticized Clinton for, as a U.S. senator, voting in favor of the 2003 U.S.-led invasion of Iraq. Trump expressed early concerns about the operation's cost.

Another political millstone could be a 2012 Defense Department inspector general's report that said Stavridis had failed to obtain prior authorization to use a government aircraft during an unofficial trip and submitted improper travel expenses. Stavridis was cleared of misconduct.

Stavridis would bring military heft to Clinton's presidential ticket. Trump is considering Michael Flynn, a retired U.S. Army lieutenant general and former director of the Defense Intelligence Agency, for the No. 2 spot.

Flynn, a Democrat who is nonetheless fiercely critical of Obama's foreign policy, would be an unconventional choice for Trump. The wealthy New York businessman is formally vetting former U.S. House of Representatives Speaker Newt Gingrich, New Jersey Governor Chris Christie and Indiana Governor Mike Pence.

Other potential vice presidential picks said to be on Clinton's short list are U.S. Senators Elizabeth Warren of Massachusetts and Tim Kaine of Virginia, according to news reports. Clinton campaigned alongside Warren in Ohio last month and is set to campaign with Kaine in his home state on Thursday. Her campaign has not confirmed that either is being formally vetted.

(Reporting by Amanda Becker; Additional reporting by Jonathan Landay, John Walcott, Phillip Stewart and Emily Stephenson; Editing by Leslie Adler and Jonathan Oatis)