Pellegrini: You never win a title in December
City trailed Jose Mourinho's side by eight points earlier in the season but have cut that gap to three with a run of five successive league wins.
A home victory over Crystal Palace on Saturday would see the reigning champions move level on points with Chelsea for at least 48 hours, with the London club facing Stoke City at the Britannia Stadium on Monday.
And Pellegrini believes his team can take confidence from last season, when Arsenal topped the table for several months before falling away badly in the second half of the campaign.
"I think Arsenal last season had a very similar number of points as Chelsea have now," said the Chilean.
"So we'll see what happens in the second half of the season and how many points you need to win.
"We don't know. Maybe Arsenal last season couldn't do it in the second half, but we don't know what Chelsea will do this year. I think that we must try and think about our team and not the others.
"We always believed that we could make up the points [last season], because we had so many games to play."
Chelsea's superb start to the campaign, which saw them avoid defeat in their first 14 matches, prompted suggestions they could canter to league glory.
Yet Pellegrini added: "You never win a title in December. Maybe you can be the best team and winning all the games, but you don't know what will happen in the second half of the season.
"So we have a lot of points to fight for. Our team always continues trusting in the way we play and the things we do."