Talks have accelerated between Arsenal and the Italian club over the past few days and Maitland-Niles could even fly to Rome on Wednesday to complete the move.
The plan is for the midfielder to join the Italian side on a straight loan deal until the end of the current season.
Maitland-Niles would then return to Arsenal in the summer, when he would have one year remaining on his current contract.
The Gunners, however, rejected approaches from the Toffees and the England international stayed put.
Arsenal have accepted Roma’s offer now, though, and Maitland-Niles will link up with Jose Mourinho in Italy as he looks to kickstart his career.