Sane, making his first league start for Pep Guardiola's side this term, opened the scoring inside two minutes with a simple tap-in from Fernandinho's pass. According to The Times, Sterling, who now earns £175k a week, wants a 100k a week pay rise which would see him become one of the highest paid players in the Premier League.
Bernardo Silva orchestrated a lot of City's good play and it was the Portuguese who set up the second, brilliantly keeping the ball in play to tee up Aguero.
"I'm relaxed at the moment, I train hard and when the manager gives me an opportunity I show him what I can do".
Pep Guardiola's champions remain in touch with early pacesetters Liverpool and Chelsea, two points off the Premier League summit in third.
"Even in this period when he didn't play, we never had doubts about Leroy's quality", the City boss told a news conference.
'It was frustrating to not put more chances into the back of the net - we need to be more ruthless.
"But we can not forget, sometimes this kind of thing happens. I'm delighted for his performance and [give him] a big compliment".
City's own setback was an ankle injury to Sergio Aguero, which saw him replaced in the second half, and Guardiola is unsure whether he will be fit for Wednesday's Champions League opener against French side Lyon. When he fell down, he felt something.
Fulham were relieved to see City take their foot off the gas in the second half, although the defeat means this is their second-worst start to a Premier League campaign.
"He could play but after 3-0, no risk".
City were able to drop down a gear without surrendering any of their control over the game, and they continued to create chances too with Sterling and Jesus both failing to hit the target.
Can someone please go and let the Premier League, the FA, UEFA, FIFA and the Court for Arbitration of Sport no about this please and help get the title taken off of City.
"It's a challenge for all of them and a challenge for me and them is to keep that level".
"Everybody is here because after three seasons, I want to work with them".