The former Juventus and Manchester United midfielder is free to play again after serving an 18-month doping ban.
Pogba is a free agent after being released from his contract at Juve by mutual consent earlier this year.
The Washington Post says contact has been established between Pogba's camp and DC United after moving to MLS in midseason this summer.
For their part, DC United refused to deny the reports yesterday.
On social media, also yesterday, Pogba teased: "Just a quick message. Nothing to show you, really. Just someone who is still hungry to come back. I trained alone, but I never gave up and I always chased my dream and what I want to achieve.
"A message to you guys: if you don't have what you want now, keep trying until you do. It could happen tomorrow, in a year, in two years. What's meant to happen will happen. See you very soon."