The article claims that Roma's sporting director, Tiago Pinto, has made an enquiry regarding the midfielder.
An option of a four-year contract has been discussed for the midfielder, who is keen on a move to the Stadio Olimpico.
Maitland-Niles has been vocal on social media discussing his lack of game time in recent months, saying on Instagram: "All I want to do is go where I'm wanted and where I'm going to play."
The 24-year-old could still stay in the Premier League though, with Everton also said to be interested in making another move for him, after their initial plan to sign him on a loan deal last summer was blocked.
Mikel Arteta is an admirer of the player, despite his lack of game time and spoke about his best attributes after making his most recent start in a 1-0 win over Watford.
"I see a different player in terms of his urgency, his commitment and the clarity in his play and purpose," Arteta said. "Since we made the decision I was clear with what I was seeing, I wanted him to stay because he was going to be useful.
"He has a huge talent which is he is versatile enough to adapt to any position on the pitch."
Maitland-Niles has made a total of 132 appearances across all competitions for the Gunners, and spent the second half of last season out on loan at West Bromwich Albion.
Watch this space in the coming weeks.