It is claimed by the report that the Italian club found a difficult negotiation process with the player’s entourage but developments in recent days have given them great encouragement that a deal can be done.
The Spanish playmaker is drawing the curtain on his decade-long stay in Manchester after this month’s Champions League games are completed, and will be available as a free agent.
Silva scored six goals and provided 11 assists for City this term, with Football Italia reporting last month that he had dinner with Lazio director of sport Igli Tare.
The 34-year-old has amassed 434 appearances for City, scoring 77 goals, providing 137 assists and winning four Premier League titles after joining from Valencia in 2010, but is out of contract this summer.
The playmaker has retired from international duty but won a notable 125 caps for La Roja, scoring 25 goals and winning three major tournaments – winning two European Championship crowns alongside the 2010 World Cup.
A product of Valencia’s youth system, Silva played for Los Che across six seasons and also enjoyed loan spells at Eibar and Celta Vigo.