"The two (Manchester) teams can't both take three points, so every time you get an opportunity to get close, you have to take it," Azpilicueta told Sky Sports.
"We have to be intelligent to look at ourselves and then we'll see how the opponents will react."
After a sloppy start to the season, Antonio Conte's Chelsea have collected six wins in last seven league games, with their only dropped points coming against Liverpool in a 1-1 draw at Anfield last month.
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The festive fixture list looks a good chance for Chelsea to collect a healthy points haul as they are set to face opponents outside the top six in their next six league matches.
West Ham are second from bottom and have not won in their last eight league games.
"We have to go game by game in this busy period in December - every three days you are fighting for a big three points. We have to look at ourselves," Azpilicueta added.
"We will then see where we are in the final weeks of the season, where we could fight for it."
(Reporting by Hardik Vyas in Bengaluru; Editing by Keith Weir)
