The news came after manager Jose Mourinho had told reporters that captain John Terry would return from injury at Charlton Athletic on Saturday.
Cole was carried off on a stretcher during Wednesday's league win over Blackburn Rovers after injuring his posterior cruciate ligament in his left knee.
Terry, who has been out since December 13 with a back problem that required surgery, has been sorely missed in defence for the champions, who are six points behind leaders United in second place.
"He will return this weekend," Mourinho told a news conference at the team's training ground. "He's an important player, he's been out for a long, long time. It's important he's back, especially when we keep losing players."
Chelsea's treatment room has been kept busy throughout a demanding campaign.
"When a player recovers we lose another and that's what we have had all season," Mourinho said. "But we are strong and are in four competitions.
STRONG GROUP
"We are six points behind and I think that at the moment that's very, very good. It's a big achievement from a group full of problems, problems that look like they will never end.
"But the group is strong. It resists and fights against a difficult situation. We are there."
Despite the woes, which include losing wingers Joe Cole and Arjen Robben, Mourinho said his squad still felt buoyant about their chances of winning a third consecutive league title.
"We've done very well to be in this situation at the end of January and we think we can improve. We think we can do it," he said.
Mourinho's only regret is that his side must wait until April before coming face to face with United again at Stamford Bridge, having drawn 1-1 at Old Trafford on November 26.
"For me, it's a pity we can't play Manchester United soon," said the Portuguese coach. "Because if we play soon and if we can reduce the gap from six to three, everything is open."
"But we have to wait...and try to keep this distance."
Mourinho again batted away speculation over his own future, following reports in the British media that he might leave at the end of the season.
Having said last May that he had considered quitting, Mourinho said: "I've much more enjoyed this season... It's encouraged me to stay."
(Additional reporting by Sylvia Westall)
