The 33-year-old suffered concussion when he was knocked unconscious during the victory over Norwich City and is yet to return to full training after resting over the international break.
Andre Villas-Boas, the Chelsea manager, has also confirmed the former Marseille forward will miss the Champions League clash against Bayer Leverkusen next week.
"He has to be authorised medically to make his full return to training," said Villas-Boas.
"He has been doing light sessions, of course, with our physios. Let's push it to the limit to try for him to be available for Man United. I wouldn't say he would be available for Leverkusen."
Drogbas injury means Fernando Torres is likely to start his fourth Chelsea game in a row this season, which would give him the chance to get over the disappointment of being dropped from Spains matchday squad for the Euro 2012 qualifier against Liechtenstein.
Daniel Sturridge, who was on loan at Bolton last season, also comes into contention after returning from suspension.
"Sturridge never stopped training since we started," Villas-Boas said.
"He is very competitive in training. You saw the part he could play in pre-season and at Bolton. It's a plus that he is on for selection and can add to the team as well."
Villas-Boas squad was bolstered on transfer-deadline day with Raul Meireles arrival from Liverpool, while Yossi Benayoun left for Arsenal.
"We spoke about wanting to fill a space in midfield and bring one more in," he said.
Villas-Boas task now is to inspire his team to challenge Manchester United and Manchester City following their blistering starts to the campaign.
"They've scored a lot of goals and that's good for British football," he said. "We just hope to score one more than the opponents.
"We've discussed this before, that there are five teams challenging. And I wouldn't be stupid enough to leave Tottenham out, it's not impossible they can join the group and challenge."
Chelsea are two points off the pace ahead of their trip to the Stadium of Light for a match they are expected to win.
Sunderland have not beaten Chelsea on home soil in seven meetings spanning almost 11 years as they go in search of their first victory of the season.
They have found the net just once in six-and-a-half hours so far to put Steve Bruce in danger of becoming the first manager under the unwanted spotlight, especially given his significant summer spending in the transfer market, which has seen 11 new arrivals.
The hosts are likely to be without John O'Shea, the defender who was injured on international duty with the Republic of Ireland.
Nicklas Bendtner, the Denmark forward signed on a season's loan from Arsenal, is expected to make his debut up front in an effort to improve a goal threat which has so far been sadly lacking.
"We know how difficult a team like Chelsea will make it for us," Wes Brown, Sunderland's former England and Manchester United defender, said.
The 31-year-old added: "But we're at home and we want to show our fans just what we can do."
Source: AFP
Source: AFP