The Athletic was the first to report the news.
The DCU job became open after manager Wayne Rooney left his position earlier this month following the conclusion of the Black-and-Red's league season, one in which the team failed to make the MLS Cup playoffs for the fourth year running.
Arena, 72, resigned as both manager and sporting director of New England last month. The club had placed him on administrative leave on July 30 pending an investigation into allegations that he made "insensitive and inappropriate remarks."
At the time of his resignation, Arena said that he made the decision after "much soul searching."
He added: "I know that I have made some mistakes and moving forward, I plan to spend some time reflecting on this situation and taking corrective steps to address what has transpired. And while this has not been an easy decision, I am confident that it is in the best interest of both the New England Revolution organization and my family that we part ways at this time."
There are still multiple steps that would have to be completed for Arena to be considered for the post. At the time of his resignation, MLS released a statement indicating that the investigation "confirmed certain of these allegations" and that for Arena to work in the league again "he must first submit a petition to" MLS commissioner Don Garber.
D.C. United is also conducting a search for the next general manager, a position that has been vacant since Lucy Rushton was dismissed a year ago. DCU has made clear that the GM, once hired, will lead the search for the team's next manager.
A source confirmed to ESPN a report in The Athletic that Columbus Crew assistant GM Issa Tall, Nashville SC assistant GM Ally Mackay and Orlando City assistant GM Ricardo Moreira are all candidates for the GM job.
He won MLS Cup titles with D.C. United in 1996 and 1997 and with the Galaxy in 2011, 2012 and 2014. He has also won four Supporters' Shields -- two with the Galaxy and one each with New England and DCU -- as well as a U.S. Open Cup crown with D.C. United.
He has had two stints with the U.S. men's national team, and won five NCAA Division I championships over 18 seasons at the University of Virginia.