The Italian club's sporting director Tiago Pinto had made contact with the north London club last month to explore a potential move, ESPN had previously reported, and talks have progressed positively since.
It is understood Maitland-Niles will join Roma until the end of the season, but the deal does not contain an option or an obligation for a permanent move the 24-year-old.
Negotiations are ongoing, but all parties expect an agreement to be reached soon. Maitland-Niles almost left Arsenal in the summer with Everton hoping to sign the midfielder, but he stayed at the club following last-ditch talks with manager Mikel Arteta.
Roma were interested in exploring an option to sign Maitland-Niles and had discussed the possibility of a four-year contract with the player but Arsenal have so far only willing been to sanction a temporary deal. Maitland-Niles' existing deal with the Premier League club expires in 2023.