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.
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 2012-2014.
He has spoken in the past about wanting the United States to work more closely with Russia to resolve global security issues.
Flynn told Russia Today in an interview published on Dec. 10 that the United States and Russiashould work together to resolve the Syrian civil war and defeat Islamic State.
Flynn has a book coming out next week, co-written with Michael Ledeen, titled: "The Field of Fight: How We Can Win the Global War Against Radical Islam and Its Allies."
Related news:
> Two leading Republicans shy away from being Trump's VP pick