The Chelsea legend is in line for a start on Sunday at Old Trafford as the side have suffered injuries to two of their strikers lately.
Costa hasn't played the two games since returning from international duty as his hamstring troubles are well-documented, whilst Remy suffered a groin injury scoring the opening goal in Chelsea's 6-0 win over Maribor in the Champions League in midweek.
Drogba managed to score his first goal since returning to the club from the penalty spot against Maribor and is aware of the threat that Manchester United pose during Sunday's encounter.
He told the Chelsea website: "They are a threat. We know to go there with our belief and our strength, but we also have to know that they’re a good team."
A lot has been mentioned about the talent United have going forward having signed Angel Di Maria and Radamel Falcao in the closing stages of the transfer window, but their deficiencies at the back have been exploited so far this season.
Chelsea's defence hasn't been as tight as Jose Mourinho will have liked it to be so far this season as he prepares to face up to one of his former bosses in Louis van Gaal, but against Arsenal earlier on in the season they put in a performance that Mourinho's sides have often been renowned for by remaining compact at the back, and not giving their opponents a sniff of goal.
Last season at Old Trafford, Mourinho started the 0-0 draw without a recognised striker so his place in the starting XI isn't completely set in stone for Sunday.
The forward added: "It’s up to the manager to decide who is going to start.
"I need time because before signing here I hadn’t played much for two or three months. I’ve also had an injury that kept me out for a while so I need more games but I’m training hard to be back to full fitness."