The Spain international is said to be reluctant to sign a new deal at the Etihad Stadium, as he would have to take a drop in wages.
Luciano Spalletti's side are also interested in Mangala and may find it easier to bring the defender to San Siro.
City were said to be keen to sell him last summer, while he is thought to desire a move to Serie A, per Fissler.
Silva's deal expires in 2019, and he has shown an interest in a move to AC Milan, per TuttoMercatoWeb (h/t the Daily Mirror).
The 31-year-old remains a key figure for Manchester City and continues to have an influence on the team, as highlighted by Squawka:
Squawka Football @Squawka
David Silva in the Premier League this season: • Most chances created (23) • Most assists (6) No hair, don't care. 🙌 https://t.co/W960uC7RNv2017-9-24 06:26:00
However, manager Pep Guardiola has no shortage of options—namely Kevin De Bruyne and Bernardo Silva—and would not struggle for replacements were Silva to decide to leave.
De Bruyne, in particular, has been in superb form recently and was the key man in City's 1-0 win over champions Chelsea on Saturday, per football writer Liam Canning:
Liam Canning @LiamPaulCanning
Fair play to Manchester City. Totally outclassed Chelsea from start to finish. Deserve their win. Kevin De Bruyne ran the show. Top player.2017-9-30 18:23:11
Yet Silva is widely regarded as one of City's greatest-ever players and has helped them to two Premier League titles and an FA Cup.
His vision and touch mean he is often the architect of City's attacking play, and the club will surely want to keep hold of him, particularly considering he still seems to be at the peak of his powers.
It may be a different scenario for Mangala, however, as the centre-back has managed just 19 minutes in the Premier League for the club this season, per WhoScored.com.
The 26-year-old joined from FC Porto in 2014 but has never managed to nail down a regular place in the side and spent last season on loan at Valencia.
City have looked much improved defensively this season, conceding just two goals in seven Premier League outings, largely without Mangala.
John Stones appears to be thriving in his second season under Guardiola and, like De Bruyne, put in a strong display against Chelsea, per Squawka:
Squawka Football @Squawka
John Stones' game by numbers vs. Chelsea: 97.5% pass accuracy 80 passes 5 clearances 3 aerial duels won 2 tackles won 2 interceptions 👏 https://t.co/KzJYGWTSbJ2017-9-30 21:35:00
City do not have a host of options in defence alongside Stones and Mangala, with Nicolas Otamendi and Vincent Kompany the only other senior centre-backs in the squad.
Kompany's recent injury record will be of concern to City:
Vincent Kompany: Has only featured in 32% of the last three Premier League campaigns #MCILIV https://t.co/1axo61VqN02017-9-8 15:30:03
However, if the start of the campaign is anything to go by, Mangala looks as if he will see little playing time this season and could leave in January should City receive an acceptable offer.