Roma is prepared to make a £15 million bid for the 23-year-old Republic of Ireland midfielder.
The Italian club is eager to start discussions with Sunderland to bring Neil on board, potentially making him the first signing of new coach Gian Piero Gasperini's tenure.
Gasperini has recently announced his departure from Atalanta and is now in the final stages of talks with Roma.
Neil has made 197 appearances for Sunderland, scoring 12 goals and providing 20 assists throughout his time with the team.
