Since arriving from Monaco in the summer of 2017, Silva has become an integral part of the Man City side, registering 55 goals and 59 appearances in 306 games.
During his time at the Etihad Stadium, the Portugal international has helped the club win 14 trophies, including five Premier League titles and the Champions League.
Having spent the last six years in the North West of England, there is a belief that Silva is tempted to try a fresh challenge.
Paris Saint-Germain are among those to show an interest, and they have reportedly proposed a swap deal involving Gianluigi Donnarumma and Marco Verratti.
Barcelona president Joan Laporta has stated that he "would like" to bring Silva to La Liga, while there have also been links with Al-Hilal.
The Saudi Arabian club have presented the attacker with a lucrative £500,000 a week deal, which would represent a significant increase on his current salary.
With Silva seemingly in hot demand, The Mirror are reporting that Man City are keen for the 28-year-old to put pen to paper on a new contract.
The reigning European champions have offered Silva a two-year extension and a pay rise that would take his earnings to £300,000 a week.
They are believed to be pushing the Portuguese midfielder to a final decision as they look to end the speculation surrounding his future.
Man City have already seen Ilkay Gundogan leave this summer, after the Germany international decided to join Barcelona on a free transfer following the expiry of his contract.
Riyad Mahrez is set to sign for Saudi Arabia's Al-Ahli for £34.7m, while Kyle Walker has been linked with a move to German champions Bayern Munich.
If Silva decides to leave the Etihad Stadium this summer, Pep Guardiola's side be hoping to receive a £70m fee for his services.