The elder Flynn served in his role at the White House for only 24 days before being fired for misleading Vice President Mike Pence and several others about conversations he had with Russian Ambassador Sergey Kislyak.
White House officials have previously stressed that those charged to date were campaign officials who were not brought into government by Mr Trump.
News reported on Sunday the actions are a part of Mueller's probe into possible collusion between President Donald Trump's presidential campaign and the Russian government. Flynn's son had reportedly worked closely with his father at his lobbying firm, the Flynn Intel Group.
Last week the Justice Department unsealed indictments against Trump's former campaign chairman Paul Manafort and a business partner of his, Rick Gates. Federal investigators are also reportedly looking into allegations Flynn attempted to sidestep the extradition process and send the Turkish cleric Fethullah Gülen, a rival of Turkish President Recep Tayyip Erdogan, back to Turkey in exchange for a multi-million dollar fee. Lawyers for the Flynn family did not comment to NBC on the news. Both are facing a 12-count indictment for conspiracy against the United States, laundering money, and acting as an unregistered agent of a foreign principal. It remained unclear Sunday if Mueller had plans to pursue charges against Flynn or his son. Flynn, who was sacked after just 24 days on the job for lying about his communications with the Russian ambassador, has always been a person of interest to the Justice Department for his undisclosed lobbying ties and work as a foreign agent, which allegedly continued while he was on Donald Trump's transition team.
If he is charged, Mr Flynn would be the fourth person to face prosecution as part of Mr Mueller's investigation. It was also unveiled that George Papadopoulos, a former Trump foreign policy adviser, pleaded guilty over the summer to lying to federal prosecutors.