The Blues are currently third, eight points behind the leaders but only two points behind The Gunners.
"Let's be honest, it is going to be difficult [to catch Man United] but we can put some pressure maybe on Arsenal for second place," Drogba told ChelseaTV. "Let's see, but we have to win our games."
Referring to their 1-3 away victory at the weekend, he added: "It was a good afternoon against West Bromwich. It was good to start winning again and it is important we secure third place."
Chelsea take on Birmingham at Stamford Bridge tomorrow night.