And they want Guardiola to emulate what Sir Alex Ferguson achieved across town at Manchester United by winning multiple Premier League titles as well as challenging Real Madrid and Barcelona's domination of the Champions League over the last decade.
City believe Guardiola has benefited from a hard first season in England when he under-estimated the competition and physical intensity of the Premier League and needed time to coach his players to play his way.
City also topped their Champions League group with 15 points.
"I'm not sure they are quite there", he said when asked by talkSPORT whether City were the greatest Premier League side ever.
"I know they have a huge squad, a great squad of players".
Ilkay Gundogan headed City ahead after 14 minutes and, given the chances they went on to create, it was remarkable it took Kevin De Bruyne until the 70th minute to add the second.
City had gone into the game with an 11-point lead at the top of the table and in such form they look unstoppable, but striker Jesus insists nobody in the squad is getting carried away. "They have done incredibly well with the run they have been on, but the Premier League is so hard, especially now with this Christmas period coming up". But there are so many top teams.
"Well for me, Manchester City right now are the best team in Europe", he told BT Sport.
"Since then I think we maintained that level, with ups and downs of course, for example at Bournemouth we won in the last minute and Southampton we won in the last minute, but in general we maintained that level that we started against Tottenham in pre-season... and now we've maintained that level for three or four months and that's why we are so happy".
"Regardless of if they're got the best player in the world - they haven't in Messi or Cristiano Ronaldo or the Neymars of this world - but tactically, they're on another planet to any team around".