After cruising to the title last season, Pep Guardiola's men have fallen seven points back of high-flying Liverpool in the Premier League this term.
Jurgen Klopp's charges have set a blistering pace in 2018-19, winning 17 and drawing three of their 20 league matches thus far.
Liverpool's title credentials will be put to the test on Thursday, as they travel to the Etihad to take on City in a high-profile showdown.
And Silva has admitted that the pressure will firmly be on the home side.
“We know the pressure is a little bit more on us,” Silva said. “Because if we don’t win, it will be very difficult to go after them.
"That’s what we will try to do. It is what we try to do every game. We will try to win the three points, especially with our fans, and we’ll try to win that game.”
With the pace that Klopp's side have set this season, the Portugal international knows his side can ill afford to fall further behind, and that even a draw would be far from useful.
"We have to think that we have to win every game possible to try to reach them, to close the gap a little bit and that’s what we’ll try to do in the next game," Silva said.
"We know we are seven points behind and if we win it will be only four – seven or four is very different – but we’ll put some pressure into them.”
Liverpool have been the Premier League's most impressive side in 2018-19 thus far, and Silva recognises that Klopp's side have quality all over the pitch.
“They’ve had a lot of clean sheets. An impressive defence. The front three, everyone knows how good they are," Silva said.
"They work a lot. The midfielders they work a lot, they press a lot. We know them, they know us, this season they’ve been doing very well in the Premier League and the Champions League so it’s two very good teams, and we’ll try to win the game.”