He left the military after President Barack Obama fired him from his post as head of the Defense Intelligence Agency
Highly respected as a decorated military intelligence officer helping combat insurgent networks in Afghanistan and Iraq, Flynn, 57, later generated widespread criticism for his strident backing of the Republican's campaign.
He served as Trump's leading adviser on national security issues during the campaign and was a highly visible surrogate, with a hardline stance on radical Islam.
It was not immediately clear whether Flynn had accepted the offer to become what many believe to be the country's top national security official.
As national security adviser, he would provide one of the most influential voices on foreign policy as well as some of the most pressing security issues facing the country, including the battle against the Islamic State group, China's rising challenge in the South China Sea and elsewhere, and opposition from Russia.
His role would probably be even more influential than his predecessors' thanks to Trump's near-total lack of experience in national security matters. Flynn would serve as the administration's main contact with the Pentagon, State Department and intelligence agencies, overseeing a staff of around 400 people.
He left the military after President Barack Obama fired him from his post as head of the Defense Intelligence Agency in 2014 following complaints about his leadership style.
He became a vocal critic of Obama's, blaming his sacking on the administration's unwillingness to listen to his warnings about the threat from radical Islam.
He prompted criticism for his view that Islamist militants pose global civilization an existential threat, saying the world has fallen into a struggle between "centrist nationalists" and "socialists," The Washington Post reported.
Such views are close to those of Trump, who has called for banning all Muslim visitors to the United States and advocated that Muslims in the United States be registered, subjected to loyalty tests and even deported.
Such views, and others including his denunciation of the war in Iraq, have alienated many of his former military colleagues.
As Trump's campaign adviser, Flynn led chants of "Lock her up!" against Hillary Clinton during campaign rallies and fired off numerous tweets excoriating the Democratic candidate. He apologized for one that appeared to be anti-Semitic.
Flynn's refusal to reject Trump's support for waterboarding and other torture against suspects, as well as his call to kill extremists' family members have helped generate more opposition to his appointment.
He was also criticized for traveling to Moscow last year, when he sat next to Russian President Vladimir Putin at a gala for the state-run television propaganda channel RT, a trip for which he was paid, The Washington Post reported.
However, the controversy surrounding Flynn's possible appointment may matter little to Trump because it would not require confirmation in the Senate, unlike other key cabinet posts.