Drogba struggled under Luiz Felipe Scolari and his future at Stamford Bridge appeared uncertain - but since Hiddink's arrival the 31-year-old striker has scored nine goals in 12 games.
Hiddink rested Drogba for the Barclays Premier League win over West Ham to keep his striker fresh for the trip to Camp Nou this week when Chelsea face Barca in the last four of the Champions League.
"That is the competition I know all Chelsea fans want to win, and it would be special to achieve this," Drogba said. "Last season we came so close, the width of a post, and we know it will be difficult - Barcelona are a strong team, but we are confident we can stop them."
After losing the final on penalties to Manchester United last season, Drogba wants to go one better this time around and add to his trophy haul with Chelsea.
"Since I have been a Chelsea player there are many memories that I cannot forget," Drogba added. "But I think the best is yet to come. I still want to achieve more with Chelsea and we are working hard on it every day."
Getting the better of Barcelona would be another famous win against the odds for Hiddink.
His problems include Ashley Cole's suspension, with Jose Bosingwa auditioning for the role at Upton Park, and Ricardo Carvalho out injured.
It may be a makeshift defence, but Hiddink feels his side need to show adventure themselves.
After success as an underdog with South Korea and Australia, Hiddink said: "Let's try to trick the bookies once more.
"We were focused on the West Ham game but it was not easy because everyone is thinking about Tuesday when we have this very difficult, huge clash against the best team, I think, in Europe or in the world.
"We must not drop and wait until the storm is coming. We must try to harm as well, that is always our intention in big European games.
"If we wait, we will have problems. It will be a huge game, a difficult game, but we have to try to be controlled and we must score."
Bosingwa has just returned from a hamstring injury and was given an hour against Hammers winger Luis Boa Morte.
"He is capable I think but we have to take into consideration it is different to play Messi, with all respect to West Ham," Hiddink said.
"Jose is confident, it is a huge task because in my opinion he is one of the most attractive players in terms of efficiency and to watch."
Striker Nicolas Anelka is brimming with confidence heading into the Barca game.
"We have already beaten Juventus and Liverpool, who are both big sides, we know we can do it, so now we have to beat Barcelona," he said.
"If you want to win this trophy you know you will have to be able to beat a lot of very good teams."
"It is important to get a good result in the first match. If you lose that one by a big score the tie is almost finished. So it is very important for us to get something from the Nou Camp."