The Ivory Coast striker was knocked unconscious after he was accidentally punched by the visiting Norwich City custodian John Ruddy, as the pair contested a ball on the edge of the box during the Blues' 3-1 win at Stamford Bridge two weeks ago.
Drogba was discharged on the same evening having apparently suffered a "mild concussion", but the player is still suffering the effects of the injury.
However, he missed his team-mates' public training session ahead of Chelsea's UEFA Champions League tie against Bayer Leverkusen, with André Villas-Boas cautious about his chances to face United.
"Everything was OK with the scan," revealed the Portuguese.
"He did some damage to his teeth when he fell to the ground, so we have given him two days off. He will be [fit again] around the United, Fulham, Swansea games ... hopefully United."
However, reports in the Guardian indicate that the London club will not risk Drogba against the reigning Barclays Premier League champions, which will mean that Fernando Torres could get the nod against United instead.
The Spaniard has his own problems though, with the hierarchy and squad at Stamford Bridge unhappy with some comments he made in an interview.
The Chelsea manager tried to keep a lid on the furore, saying: "I don't think it's a perspective that the manager shares, but I don't have to share my players' ideas sometimes.
"He says he didn't say that. Maybe we just have to speak about that situation and he has to see our view as well. We'd just talk, share opinions", Villa-Boas concluded.