Chelsea are currently second in the Premier League after an impressive unbeaten start to the season which has included eight wins and three draws.
Maurizio Sarri’s side beat Crystal Palace 3-1 on Sunday.
However, City have made an even better start and are two points ahead of the Blues having dropped only four points in the entire campaign.
Chelsea and City will have to play four games before they play each other at the Bridge on December 8.
And Azpilicueta thinks they can win every game between now and then – before becoming the first team to beat Pep Guardiola’s all-conquering side.
“It’s in our hands. Obviously if we don’t drop points, we have the chance to do it (on December 8),” Azpilicueta said.
“We know that to get to that chance, you have to get the three points in games like we had against Crystal Palace.
“We cannot drop points, we need to work hard, keep improving and let’s see on that day, if we have the chance to do it.
“We are happy with our results. We know that we can still do better and the League is very tough – you have to fight for every game.
“This table at the moment is something that we want – to be at the top at the end.
“We know that it’s going to be difficult, but we know how to win the Premier League and we will try.”
Sarri has overseen an incredible turnaround at Chelsea after last season’s struggles.
The Blues finished fifth and, despite winning the FA Cup under Antonio Conte, missed out on the Champions League.
And Azpilicueta thinks their rivals need to start treating them as genuine title contenders.
“It’s up to us. Last season we finished 30 points behind Man City,” he added
“The gap was massive, obviously we are closer this year. We are two points behind and it’s up to us to keep the rhythm.
“Every year. It’s harder and harder to win the League so it’s up to us.
“Our only focus is to improve during the week, to improve in the games.
“That’s been our focus since Maurizio came. We are working on that.
“Last season the run they had winning (so many) games in a row – no-one could get anywhere near them.
“It’s true we are closer, but we are in November.
“Obviously you want to be at the top but we know that in England, we have the Christmas period where we play a lot of games, you then start with the European games knockout stages (in February).
“We will see how far we will go.”