Both players sustained injuries in Sunday's 1-1 draw against Bolton in the Barclays Premier League, Drogba hurting his knee and Terry dislocating his elbow.
But the Ivory Coast striker is sure they will be fit to face United in the Russian capital next Wednesday as the Blues go in search of their first Champions League crown.
"I took a blow to my knee that was operated on (back in December), and it hurt at the time," he told French daily L'Equipe.
"I put ice on it immediately. But there is nothing serious. I will be at training this week."
On the fitness of Chelsea captain Terry, who was taken to hospital after colliding with his own goalkeeper, Petr Cech, Drogba added: "I have spoken to him - he will play in Moscow.
"No-one wants to miss this gigantic match, the match of our careers. That's the case for me anyway."
Chelsea lost out to United at the weekend in the race for the Premier League title as Sir Alex Ferguson's men secured the defence of their crown with a 2-0 win at Wigan.
United will head to Moscow looking to complete the double, but Drogba said: "This Champions League match is different.
"It will play itself out over 90 or 120 minutes, like in the FA Cup final last year (which Chelsea won 1-0 thanks to Drogba's goal in the second half of extra time).
"We know that we can beat United, we proved it again in the league a fortnight ago.
"But they deserved their title and were rewarded for their consistency. We made too many mistakes."
There has been plenty of speculation about Drogba's future at Chelsea - he was recently linked with a move to Inter Milan - but he insists the Champions League final is the only thing dominating his thoughts.
"At the moment, the only thing I have in my mind is the final in Moscow," he said.
"What will happen in June or July? I still don't know anything."
Drogba admitted earlier this season he found it hard leaving Marseille for Chelsea in July 2004, and was reported as saying he wanted to leave the London club.
He maintains his relationship with supporters in England has improved but admits he has found it difficult to settle.
"I didn't want to leave Marseille," he added.
"I had trouble getting used to Chelsea and I wanted to leave at the end of every season. Not because people were not treating me well, rather because of personal reasons.
"I have started everything again from zero in England. I had to replace a great striker in Jimmy Floyd Hasselbaink, who was a favourite at the club.
"It wasn't easy but my relationship with the English supporters has evolved.
"There was at first a dissension between us but I then understood what they expected of me. Now the rapport I have with them is like what I had with the fans at Marseille."
Drogba will be back
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