Drogba netted his ninth league goal of the season in the 4-0 demolition of ten-man Bolton on Saturday but he remains one behind Torres after the Liverpool striker also found the target against Fulham.
The Ivorian's best campaign to date has been 2006/7, when he won the golden boot with 20 league goals and ended with 33 in all competitions.
He is determined to beat that tally this time round and thinks the rivalry with Torres will spur him on to achieve greater success.
"It's nice to have this competition with Torres to finish top scorer. It's always a good challenge to be part of," Drogba told the Evening Standard.
Target"Three seasons ago I was in a race against Benni McCarthy and Cristiano Ronaldo and I managed to come out on top.
"It's a big challenge for me to finish ahead of Torres this season and gives me the desire to do more for my team."
Drogba insists it is more important for the team to do well and he is confident his partnership with Nicolas Anelka will continue to pay dividends.
"I really feel good about the way the season is going for Chelsea. The key thing is we are playing with two strikers up front and I have a lot of support," he said.
"The way we pass the ball is really good, we have really improved and that is what has made the difference.
"I would like to beat my best-ever total for Chelsea of 33 goals but it's a target as long as we keep winning games, stay top of the league and win the title at the end of the season."
LampardDrogba's magnificent start to the season has prompted Lampard to declare that he is the finest centre-forward on the planet.
The Blues midfielder believes Drogba has more strings to his bow than any of his rivals for the golden boot, including Torres
"Who knows who will score more? They are both top strikers but, for me, Didier is the best in the world because of his all-round game and the form he is in," said Lampard.
"Everyone talks about his power but maybe they don't give him the credit he deserves for his finishing. His finishing at times is different class, with his head or with his foot. He is the best striker I have ever played with.
"The thing about Didier is he's a very unselfish player. A lot of things get said about him but one thing we know in the camp is he gives everything for the team.
"He's had a lot of assists this year, which just shows he's not just interested in scoring goals, he's interested in working hard for the team, heading balls out of his own box. That's the beauty of him."