The Blues currently lie second in the league table, three points behind leaders Manchester United.
Chelsea are not in action until Monday, when they tackle Wigan, but are aware they can reclaim their crown if United drop points against The Gunners and they then go on to win their remaining games of the season.
And Drogba has set his sights on claiming glory in both competitions as the season reaches its climax.
"The most important thing is to win the Premier League or Champions League, and I think we have a good chance to do both, even if it isn't going to be easy," he said in This is London.
"We are trying to fight for the title. It's more exciting when you have a lot of intensity in each competition."