Silva’s current contract with Pep Guardiola’s side will end in 2020.
But City are keen on extending the Spaniard’s contract by a further year as they see no decline in the midfielder’s performance level of physical condition.
Silva is currently sidelined with a hamstring injury he sustained during City’s 2-0 defeat to Chelsea in the Premier League last weekend.
The 32-year-old has scored eight goals in 20 appearances for City in all competitions so far this season.
City will tackle Hoffenhiem in tonight’s Champions League fixture at home.