Michael Flynn testifies before the House Intelligence Committee on "Worldwide Threats" in Washington, February 4, 2014. REUTERS/Gary Cameron

Presumptive Republican presidential nominee Donald Trump is giving consideration to retired Lt. Gen. Michael Flynn as a potential vice-presidential running mate, a Republican source familiar with the process told Reuters on Saturday.

For weeks Trump has conducted a high-profile canvassing of Republican political stalwarts as part of his running-mate search, but he has also made clear he is looking at what a military leader would bring to the ticket.

The source, speaking on condition of anonymity, said Flynn has emerged as a possibility, confirming reports in the New York Post and The Washington Post. The Trump campaign had no comment.

Flynn, though a fierce critic of Barack Obama, is a registered Democrat, according to The Washington Post.

The thinking is that Flynn, who has been a foreign-policy adviser to Trump, would be able to help Trump in the area of national security at a time of challenges abroad like the threat from Islamic State militants.

Trump is also considering a more conventional political choice for his running mate, such as former House of Representatives Speaker Newt Gingrich, Indiana Governor Mike Pence, or New Jersey Governor Chris Christie.

Flynn was chief of the Defense Intelligence Agency under President Barack Obama from 2012 to 2014.

He has spoken in the past about wanting the US to work more closely with Russia to resolve global security issues.

Flynn told Russia Today in an interview published on December 10 that the US and Russia should work together to resolve the Syrian civil war and defeat Islamic State.

He was pictured seated at the head table just two seats away from Vladimir Putin at a dinner honoring Russia Today, a media network funded by Russia's government, reports Politico.

Flynn has a book coming out next week, cowritten with Michael Ledeen, titled: "The Field of Fight: How We Can Win the Global War Against Radical Islam and Its Allies."

(Reporting by Steve Holland; Editing by Leslie Adler and Business Insider)