City have also looked at Paris Saint-Germain's Ibrahim Mbaye and RB Leipzig's Yan Diomande among a number of other names being considered by the club's recruitment staff.
The search comes as Tottenham continue working to finalise a deal worth around £65m for City's Savinho, with Enzo Maresca's side wanting a replacement lined up before sanctioning the Brazilian's departure.
Manchester City had previously shown interest in the 26-year-old Portugal international Neto before he joined Chelsea from Wolverhampton Wanderers for £51m, and Maresca struck up a good rapport with the Portuguese during their time together at Stamford Bridge, where Neto made 52 appearances last season, contributing ten goals and ten assists across all competitions.
City also admire Chelsea full-back Malo Gusto, though they are not currently prepared to meet the club's £75m asking price for the France international. Chelsea, for their part, have already offloaded winger Alejandro Garnacho to Aston Villa on loan, with the Midlands club also keen on signing striker Nicolas Jackson, while Chelsea continue working to bring in Bayer Leverkusen winger Kerim Alajbegovic as part of their own summer rebuild under new head coach Xabi Alonso.
Maresca was formally unveiled as Pep Guardiola's successor on Friday and reflected on his previous spells in management when discussing his approach to the City job.
"I have been quite lucky in terms of my former clubs, Leicester and Chelsea I think we did a great job in both clubs. The identity of the team was clear," Maresca said. "The success of the team was clear, and I feel very lucky to be part of these clubs."
Manchester City's business this summer has already included the £116m signing of Elliot Anderson from Nottingham Forest, with further additions expected across multiple positions as Maresca looks to shape his first squad at the Etihad Stadium following Guardiola's departure after a decade in charge.